NAME DATE PERIOD. Study Guide and Intervention

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1 5-1 Study Guide and Intervention Ratios and Percents A percent is a ratio that compares a number to 100. To write a fraction as a percent, find an equivalent fraction with a denominator of 100. If the denominator is a factor of 100, you can use mental math. Examples Write each ratio or fraction as a percent. James made 65 out of 100 free throws. 65 out of % 1 4 of all high school students are not taking physics So, 1 out of 4 equals 25%. You can express a percent as a fraction by writing it as a fraction with a denominator of 100. Then write the fraction in simplest form. Example % So, 35%. 2 0 Exercises Write 35% as a fraction in simplest form. Definition of percent. Simplify. Write each ratio or fraction as a percent out of out of : : Write each percent as a fraction in simplest form % 8. 93% 9. 10% % % % Chapter 5 10 Course 3

2 5-1 Skills Practice Ratios and Percents Write each ratio or fraction as a percent out of out of out of out of out of :4 7. 2: : : : Lesson Write each percent as a fraction in simplest form % % % % % % % % % % % % % % % % Chapter 5 11 Course 3

3 5-1 Practice Ratios and Percents Write each ratio or fraction as a percent out of per of out of out of :5 8. 3:10 Write each percent as a fraction in simplest form % % % % % % % % 17. GOVERNMENT Two out of 100 U.S. Senators are from Utah. Write this ratio as a percent. 18. ARCHITECTURE Four out of the world s 25 tallest buildings are located in Hong Kong. Write this ratio as a percent. 19. POPULATION According to a recent census, the population of Montana is about 0.3% of the United States population. Write this percent as a fraction in simplest form. 20. REASONING Which is greatest: 3, 19:25, or 74%? Explain your reasoning GEOGRAPHY Five of the 50 U.S. states border the Pacific Ocean. What percent of the U.S. states border the Pacific Ocean? Chapter 5 12 Course 3

4 5-1 Word Problem Practice Ratios and Percents 1. PETS Three out of every 20 dogs in the U.S. are Golden Retrievers. Write this ratio as a percent. 2. GEOGRAPHY About 29% of the world s surface is covered by land. Write this percent as a fraction. 3. BASKETBALL Shaquille O Neal of the L.A. Lakers hit 11 out of 20 free throws in a 5-game series. Write this number as a percent. 4. EDUCATION In a recent survey, about 38% of 18- to 24-year-olds in the United States were enrolled in a college or university. Write this percent as a fraction. Lesson HEALTH CARE Over 15% of Americans do not have health insurance. Write this percent as a fraction. 7. GEOGRAPHY The federal government owns about 1 3 of the land in the state 20 of Utah. Write this fraction as a percent. 6. ENERGY Japan accounts for about 5.4% of the world s petroleum consumption. Write this percent as a fraction. 8. POPULATION In a recent survey, 11 out of every 50 people in the United States were age 65 or older. Write this ratio as a percent. Chapter 5 13 Course 3

5 5-1 NAME DATE PERIOD Enrichment Visualizing Percent Shade each grid to show the given ratio. Write the percent of the grid that is shaded and the percent that is not shaded Shaded Shaded Shaded Not shaded Not shaded Not shaded Shaded Shaded Shaded Not shaded Not shaded Not shaded Shaded Shaded Shaded Not shaded Not shaded Not shaded Chapter 5 14 Course 3

6 5-2 Lesson Reading Guide Comparing Fractions, Decimals, and Percents Get Ready for the Lesson Read the introduction at the top of page 256 in your textbook. Write your answers below. 1. Write each percent as a fraction. Do not simplify the fractions. 2. Write each fraction in Exercise 1 as a decimal. 3. How could you write a percent as a decimal without writing the fraction first? Read the Lesson Complete each sentence. 4. To write a decimal as a percent, by 100 and add the percent symbol. 5. To write a percent as a decimal, by 100 and remove the percent symbol. Lesson Dividing by 100 is the same as moving the decimal point two places to the. 7. Multiplying by 100 is the same as moving the decimal point two places to the. Determine whether each expression represents changing from a decimal to a percent or a percent to a decimal Remember What You Learned Work with a partner. Pretend your partner has not studied this lesson. On a piece of paper, write a percent and a decimal using different numbers. Teach your partner how to write a percent as a decimal and how to write a decimal as a percent. Be sure to show how to place the decimal point. Chapter 5 15 Course 3

7 5-2 Study Guide and Intervention Comparing Fractions, Decimals, and Percents To write a percent as a decimal, divide by 100 and remove the percent symbol. To write a decimal as a percent, multiply by 100 and add the percent symbol. To express a fraction as a percent, you can use a proportion. Alternatively, you can write the fraction as a decimal, and then express the decimal as a percent. Example 1 Write 56% as a decimal. 56% 56 % Divide by 100 and remove the percent symbol Example 2 Write 0.17 as a percent Multiply by 100 and add the percent symbol. 17% Example 3 7 Write as a percent. 2 0 Method 1 Use a proportion. 7 x 7 Write the proportion Method 2 Write as a decimal. Convert to a decimal by dividing x Find cross products. 35% Multiply by 100 and add the x Multiply. percent symbol x 2 Divide each side by x Simplify. 7 So, can be written as 35%. 2 0 Exercises Write each percent as a decimal % 2. 36% 3. 82% % Write each decimal as a percent Write each fraction as a percent Chapter 5 16 Course 3

8 5-2 Skills Practice Comparing Fractions, Decimals, and Percents Write each percent as a decimal % 2. 13% 3. 26% 4. 41% 5. 79% % % % % % % % Write each decimal as a percent Write each fraction as a percent Lesson Chapter 5 17 Course 3

9 5-2 Practice Comparing Fractions, Decimals, and Percents Write each percent as a decimal % 2. 40% % % % % 7. 8% 8. 3% Write each decimal as a percent Write each fraction as a percent Order each set of numbers from least to greatest , 0.5, 4%, , 6%,, %, 0.96, , %, 3 4, 1 9, Replace with <, >, or = to make a true statement % % % 32. TEST SCORES On a science test, Ali answered 38 of the 40 questions 9 correctly, Jamar answered of the questions correctly, and Paco 1 0 answered 92.5% of the questions correctly. Write Ali s and Jamar s scores as percents and list the students in order from the least to the highest score. Chapter 5 18 Course 3

10 5-2 Word Problem Practice Comparing Fractions, Decimals, and Percents 1. BASKETBALL In a recent season, Susan Bird of the WNBA team the Seattle Storm made 43% of her 3-point shots. Write this percent as a decimal. 2. POPULATION From 2000 to 2005, the population of New York City increased by 2%. Write this percent as a decimal. 3. BASEBALL Recently, the Chicago White Sox had a team batting average of Write this decimal as a percent. 4. HEALTH In 2004, 15.7% of Americans were without health insurance. Write this percent as a decimal. Lesson INTERNET Internet access in the U.S. has increased dramatically in recent years. If 110 out of every 200 households had Internet access, what percent of households had Internet access? 7. ECONOMICS Consumer prices in the U.S. rose at a rate of from 2003 to Write this decimal as a percent. 6. VOTING The rate of voter turnout in the 1932 U.S. presidential election was Write this decimal as a percent. 8. SPORTS In a recent season, the WNBA Indiana Fever won 2 1 of their 34 games. Write this fraction as a percent. Chapter 5 19 Course 3

11 5-2 NAME DATE PERIOD Enrichment Block Party 1. This model is made up of 27 cubes and has a length of 3 cubes, a width of 3 cubes, and a height of 3 cubes. The entire model will be painted yellow, then cut apart into individual cubes. What percent of the cubes will be painted yellow on: 0 sides? 1 side? 2 sides? 3 sides? 4 sides? 5 sides? 6 sides? 2. This model is made up of 64 cubes and has a length of 4 cubes, a width of 4 cubes, and a height of 4 cubes. The entire model will be painted orange, then cut apart into individual cubes. What percent of the cubes will be painted orange on: 0 sides? 1 side? 2 sides? 3 sides? 4 sides? 5 sides? 6 sides? 3. This model is made up of 125 cubes and has a length of 5 cubes, a width of 5 cubes, and a height of 5 cubes. The entire model will be painted purple, then cut apart into individual cubes. What percent of the cubes will be painted purple on: 0 sides? 1 side? 2 sides? 3 sides? 4 sides? 5 sides? 6 sides? Chapter 5 20 Course 3

12 5-2 Scientific Calculator Activity The Percent Key The percent key interest equations. 2nd [%] on a calculator can be used to solve simple Example Find the simple interest to the nearest cent. $265 at 5.15% for 2 years I prt I $ % 2 ENTER Enter: nd [%] The solution is $ Exercises Find the simple interest to the nearest cent. Write an equation in the form I prt. Then use the percent key to solve. 1. $1,000 at 6.75% for 5 years 2. $535 at 8.2% for 6 months 3. $257 at 15% for 2.5 years 4. $48.67 at 12.25% for 30 months Lesson Terry put $500 in a savings account that earned 5.125% interest. She has not made any deposits or withdrawals for 7 years. How much interest has she earned? 6. How much money will be in Terry s account at the end of 15 years if she does not make any deposits or withdrawals? 7. Suppose you deposit $200 in an account that earns 10% interest. How many months will it take to earn $50 in interest? 8. How much money would you have to deposit in an account that earns 8.375% interest to earn $1,000 in interest in 18 months? Chapter 5 21 Course 3

13 5-3 Lesson Reading Guide Algebra: The Percent Proportion Get Ready for the Lesson Complete the Mini Lab at the top of page 263 in your textbook. Write your answers below. 1. What is 40% of 5? is 80% of what number? part Draw a model and find what percent 7 is of Read the Lesson 4. Look at page 263 in your textbook. Fill in the blanks to complete the percent proportion. whole percent 100% 5. Complete the table for each statement or problem. For a quantity that needs to be found, put a question mark in the appropriate column. a. 14 is 20% of 70. b. 6% of 40 is 2.4 c. 13 out of 25 is 52% d. What is 30% of 65? e. Find 41% of 250. f. What percent of 25 is 18? Remember What You Learned part whole percent 6. Use a clean sheet of paper and Examples 1 3 on pages 263 and 264 in your textbook. Starting with Example 1, cover up everything in the example with your paper except the title and its question. Now try to work the problem without looking at the book. Then compare your work to the work in the book. Repeat this with the other two examples. Chapter 5 22 Course 3

14 5-3 Study Guide and Intervention Algebra: The Percent Proportion You can use a percent proportion to find a missing part, whole, or percent. part percent w hole Example 1 12 is what percent of 60? part w hole p } percent 100 Replace a with 12 and b with p Find the cross products. 1,200 60p Multiply. 1, p 6 0 Divide each side by p 12 is 20% of 60. Example 2 What number is 40% of 55? part w hole a } percent Replace p with 40 and b with 55. a Find the cross products. a 22 Use similar steps to solve for a. So, 22 is 40% of 55. Exercises Write a percent proportion and solve each problem. Round to the nearest tenth if necessary is what percent of 10? 2. What number is 15% of 40? is 75% of what number? is what percent of 200? 5. What number is 65% of 120? is 13% of what number? is what percent of 56? 8. What number is 12.5% of 88? Lesson is 92% of what number? is what percent of 66? 11. What number is 31.5% of 200? is 54% of what number? Chapter 5 23 Course 3

15 5-3 NAME DATE PERIOD Skills Practice Algebra: The Percent Proportion Write a percent proportion and solve each problem. Round to the nearest tenth if necessary is what percent of 5? 2. What number is 25% of 40? is 60% of what number? 4. What percent of 8 is 6? 5. Find 15% of is 33% of what number? is what percent of 150? 8. What number is 30% of 140? is 60% of what number? 10. What percent of 60 is 42? 11. Find 90% of is 35% of what number? is what percent of 45? 14. What number is 75% of 44? is 40% of what number? 16. What percent of 40 is 15? 17. Find 5% of is 60% of what number? is what percent of 69? 20. Find 55% of is 44% of what number? is what percent of 20? 23. What number is 85% of 40? is 18% of what number? Chapter 5 24 Course 3

16 5-3 Practice Algebra: The Percent Proportion Write a percent proportion and solve each problem. Round to the nearest tenth if necessary is what percent of 24? is what percent of 375? 3. What is 20% of 80? 4. What is 14% of 440? is 35% of what number? is 63% of what number? is what percent of 14? 8. Find 350% of What percent of 120 is 24? 10. What percent of 84 is 6? 11. What is 7.5% of 225? is what percent of 660? is 21.1% of what number? 14. Find 6.4% of What percent of 160 is 1? is 12.5% of what number? 17. GAMES Before discarding, Carolee has 4 green cards, 3 red cards, 3 orange cards, and 1 gold card. If she discards the gold card, what percent of her remaining cards are red? Lesson 5 3 Chapter 5 25 Course 3

17 5-3 Word Problem Practice Algebra: The Percent Proportion 1. COMMUTING On his trip across town, Mark was stopped by a red light at 9 out of 15 intersections. At what percent of intersections was Mark stopped by a red light? 2. CLIMATE In Las Vegas, Nevada, the skies are clear on 92% of the days. How many days in the month of June would you expect the skies to be clear in Las Vegas? Round the answer to the nearest day. 3. POLLING A recent poll shows that 65% of adults are in favor of increased funding for education. The number of adults surveyed for the poll was 140. How many of the adults surveyed were in favor of increased funding for education? 4. FLOWERS Mika s rosebush had 24 blooms in the first week of May. This was 80% as many blooms as Tammy s rosebush had during the same period. How many blooms did Tammy s rosebush have? 5. SPORTS In a recent season, the San Francisco Giants won 75 out of 162 games. What percent of their games did they win? Round to the nearest tenth if necessary. 7. DRIVING TEST On the written portion of her driving test, Sara answered 84% of the questions correctly. If Sara answered 42 questions correctly, how many questions were on the driving test? 6. GOLF On a recent round of golf, Shana made par on 15 out of 18 holes. On what percent of holes did Shana make par? Round to the nearest tenth if necessary. 8. EDUCATION In a certain small town, 65% of the adults are college graduates. How many of the 240 adults living in the town are college graduates? Chapter 5 26 Course 3

18 5-3 NAME DATE PERIOD Enrichment The Cost of Using The percent proportion can be used to describe the percent by which something depreciates, or loses its value during the course of time. Example 1 In 2006, the average purchase price of a new compact automobile was $17,000. One year later, the compact automobile that was purchased new in 2006 typically was worth $11,500. By what percent did the automobile depreciate during the first year of ownership? First find the amount of decrease. $17,000 $11,500 $5,500 Then write and solve the percent proportion. $5,500 is what percent of $17,000? 5,500 r 1 7, ,000 17,000r Exercises 32.4 r The automobile depreciated about 32.4%, or about 1 3 of its value, during the first year of ownership. Advertisements such as these regularly appear in the classified pages of newspapers. Find the percent of depreciation to the nearest tenth in each advertisement. 1. For sale: Venus 2 dr, 5 speed, air, sport wheels, mint. Bought new 8 months ago for $9,600, yours for $7,200. Must sell baby on way. 3. For sale: Mars 4 dr, auto, air, ABS, the works. 1 year old 12,400 mi. Purchase price $16,000. Your price $12,800 firm. 2. For sale: Washer/dryer combo. Antique white, electric, like new 18 mos. old. Paid $950, asking $ For sale: Dishwasher, 2 racks, full factory warranty. Never used won in contest. List: $840. I will deliver for $588 cash. Lesson For sale: Mountain bike. 20-inch frame new tires. Used but not abused. Bought last summer for $320. $150 or best offer. 6. For sale: Personal Computer. Intex processor. 8.0 GB hard drive. 56X CD-ROM drive. 17-inch monitor. Color inkjet printer with lots of software. $2,200 new yours for $895. Chapter 5 27 Course 3

19 5-4 Lesson Reading Guide Finding Percents Mentally Get Ready for the Lesson Read the introduction at the top of page 268 in your textbook. Write your answers below. 1. Seventy-five percent of the dimes she collected were minted after the year How could you find 75% of 120 mentally? 2. Use mental math to find the number of dimes minted after the year If 25% of the dollars she collected were Sacagawea dollars, use mental math to find the number of Sacagawea dollars she collected. Read the Lesson 4. Complete the following table. Percent Fraction Decimal 25% Complete each statement % of 25 of 25 or of 36 1 of 36 or % of 48 of 48 or of of 89 or Remember What You Learned 9. Work alone or with a partner. Look at the Percent-Fraction Equivalents table at the bottom of page 268 in your textbook. Create your own table on a sheet of paper or poster paper. Underneath each equivalent percent and fraction, write an example in which knowing the fraction helps you find the percent mentally. Chapter 5 28 Course 3

20 5-4 Study Guide and Intervention Finding Percents Mentally To find 1% of a number mentally, move the decimal point two places to the left. To find 10% of a number mentally, move the decimal point one place to the left. Example 1 Find 1% of % of of 195 or 1.95 Example 2 Find 10% of % of of 3.9 or 0.39 When you compute with common percents like 50% or 25%, it may be easier to use the fraction form of the percent. It is a good idea to be familiar with the fraction form of some of the common percents. 25% % % % % % % % % % 3 10 Example 3 75% % % % % 7 10 Find 25% of % of 68 1 of 68 or 17 4 Example 4 Find 33 1 % of % of 57 1 of 57 or 19 3 Exercises Compute mentally. 80% % % % % of % of % of 34 Lesson % of % of % of % of % of % of % of % of % of 45 3 Chapter 5 29 Course 3

21 5-4 Skills Practice Finding Percents Mentally Compute mentally % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of 64 2 Chapter 5 30 Course 3

22 5-4 Practice Finding Percents Mentally Compute mentally % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of % of 18.4 Replace each with <, >, or = to make a true statement % of 40 40% of % of 85 1% of POPULATION The state of New York has a population of about 20,000,000 people. About 25% of the population of New York is under 18 years old. How many people in New York are under 18 years old? 20. LIVESTOCK In 2004, there were about 60,000,000 pigs and hogs in the United States. About 10% of the pigs and hogs were in Minnesota. How many pigs and hogs were in Minnesota in 2004? MUSEUMS For Exercises 21 23, use the following information. The graph shows the percents of men, women, and children visiting a modern art exhibit at a local museum. Suppose 600 people visited the exhibit. 21. How many men visited the exhibit? 22. How many women visited the exhibit? 23. How many children visited the exhibit? Museum Visitors % Children Women 50% Men 1 33 % 3 Lesson 5 4 Chapter 5 31 Course 3

23 5-4 Word Problem Practice Finding Percents Mentally 1. ELECTIONS In a certain small town, 80% of the adults voted in the last election. How many of the 600 adults living in the town voted in the last election? 2. FISH POPULATION Fish and game managers have determined that 10% of the approximately 3,400 fish in Avondale Lake are catfish. How many catfish are there in Avondale Lake? 3. SURVEYS In a recent survey, 1% of the people had no opinion on the topic. How many of the 1,100 people surveyed had no opinion on the topic? 4. BAND In a local middle school, 33 1 % of 3 the students are in the band. There are 240 students in the school. How many middle school students are in the band? 5. AIR TRAVEL At one large international airport in the U.S., 20% of the arriving flights are from other countries. On a recent day, 240 flights arrived at the airport. How many of these flights were from other countries? 7. FARMING Jake grows corn and soybeans on his farm. He has corn growing on 66 2 % of his 330 acres. How many acres 3 are being used for corn? 6. TELEPHONE Ramona likes to keep track of her incoming calls. Last month, 25% of the 132 calls Ramona received were from her mother. How many calls did Ramona get from her mother last month? 8. ENERGY The U.S. has 25% of the nuclear power plants in the world. How many of the world s 416 nuclear power plants are in the U.S.? Chapter 5 32 Course 3

24 5-4 NAME DATE PERIOD Enrichment Using Percent to Compare Areas The area of the smaller triangle at the right is 50% of the area of the larger triangle. The smaller triangle has a base of 6 units and a height of 3 units; its area is 9 square units. Since the area of the smaller triangle is 50% of the area of the larger triangle, the area of the larger triangle is 18 square units. 1. The area of this square is 25% of the area of a larger square. Determine the dimensions and draw the larger square The area of this rectangle is 150% of the area of a smaller rectangle. Determine the dimensions and draw the smaller rectangle The area of this circle is 1,600% of the area of a smaller circle. Determine the dimensions and draw the smaller circle. 4. The area of this rectangle is 60% of the area of a larger rectangle. Determine the dimensions and draw the larger rectangle. 4 Lesson Chapter 5 33 Course 3

25 5-5 Study Guide and Intervention Problem-Solving Investigation: Reasonable Answers In the four-step problem-solving plan, remember that the last step is to check for reasonable answers. Understand Plan Solve Check Determine what information is given in the problem and what you need to find. Select a strategy including a possible estimate. Solve the problem by carrying out your plan. Examine your answer to see if it seems reasonable. Example The cost of a guitar is $300. Margaret works at the music store and can buy the guitar for 65% of the price. Will she have to pay more or less than $200? Understand Plan You know the cost of the guitar. Margaret can buy the guitar for 65% of the price. You want to know if the guitar will cost more or less than $200. Find a close estimate. 65% is close to 66.66% or 2. Multiply the cost by the 3 estimate. $300 2 $200 3 Solve Think. $300 2 $ % is less than 66.66%, so she will have to pay 3 less than $200. Check Find 65% of $300. $ $195. Exercises $195 $ The answer is reasonable. For Exercises 1 5, determine a reasonable answer. 1. JOBS Maxine is paid $9.25 an hour to work at the bookstore. If she is saving to buy a new video game system that costs $360, will she have to work 30, 40, or 50 hours? 2. MONEY Jeff brings $120 to purchase winter clothes. He buys a coat for $ He wants to purchase a pair of jeans for $28.95 and a pair of boots for $ Does he have enough money with him to make these two purchases? 3. SURVEY In a recent survey, 56% of students at Trenton Middle School work at part-time jobs during the school year. If there are 1,378 students in the school, is 550, 650, or 750 a reasonable estimate for the number of students who work part time during the school year? 4. SHOPPING Byron took $80 to the mall to buy gifts. He spent $28.73 on a video game. He wants to purchase a book for $13.89 and a laptop bag for $ Does he have enough money with him to make these two purchases? 5. ATTENDANCE There are 1,200 students at Hillsboro Middle School. If 43% of the students attend an exhibit given by the art department, would the number of students who attended be 924, 516, or 430? Chapter 5 34 Course 3

26 5-5 Skills Practice Problem-Solving Investigation: Reasonable Answers For Exercises 1 12, estimate and rewrite the problem to determine a reasonable answer % of % of % of 1, % of % of % of % of 2, % of % of 4, % of % of 1, % of 620 For Exercises 13 24, estimate and rewrite the problem to determine a reasonable answer. 13. $54.87 $ $22.38 $ $94.67 $ $88.88 $ $7.87 $ $74.78 $ $37.42 $ $28.69 $ $ $ $89.99 $ $ $ $46.22 $86.86 Lesson 5 5 Chapter 5 35 Course 3

27 5-5 NAME Practice DATE PERIOD Problem-Solving Investigation: Reasonable Answers Mixed Mixed Problem Solving Use the reasonable answer strategy to solve Exercises 1 and MONEY After Latoya gave 35% of her allowance to her brother and 25% of her allowance to her sister, she had $12 left. How much was Latoya s allowance? 1. POPULATION About 9.5% of the population of New Mexico is Native American. If the population of New Mexico is 1,874,614, would the number of Native Americans living in New Mexico be about 180,000, 360,000, or 900,000? 2. HOMES Mr. and Mrs. Whatley want to buy a new home for $245,000. The bank requires 20% of the price of the home as a down payment for the loan. Should the Whatleys plan to pay $5,000, $25,000, or $50,000 as the down payment? Use any strategy to solve Exercises 3 6. Some strategies are shown below. PROBLEM-SOLVING STRATEGIES Work backward. Look for a pattern. Draw a diagram. 3. SPORTS Three teams participating in a track meet have 25 members, 29 members, and 33 members. The coach of the hosting team wants to have three bottles of water for each athlete. If each case of water contains 24 bottles, should the coach buy 4, 12, or 20 cases of water? 5. ELECTIONS A county with 31,500 registered voters is buying new voting machines. State law requires that the county have one polling place for every 750 registered voters and 4 voting machines per polling place. How many new voting machines should the county order? 6. GEOMETRY Brandon is drawing a rectangle similar to the one below except that each side of his rectangle is times longer. Find the area of Brandon s rectangle. 8 cm 2.4 cm Chapter 5 36 Course 3

28 5-5 Word Problem Practice Problem-Solving Investigation: Reasonable Answers For Exercises 1 8, determine a reasonable answer. 1. SHOPPING A coat that normally costs $90 is on sale at 45% off. If Jared brings $45 with him, will he have enough to purchase the coat? Explain. 2. MONEY Helen took $100 to the store. She spent $44.56 on a video game. She wants to buy a CD for $18.79 and a book for $ Does she have enough money with her to make these two purchases? Explain. 3. SCHOOL There are 438 students at Newton Middle School. If 38% of the students participate in after-school sports, would the number of students involved in sports be about 110, 170, or 220? Explain. 4. JOBS Fredrick is paid $12.35 per hour at his part-time job at a landscaping company. If he is saving to buy a new MP3 player that costs $289, will he have to work 20, 25, or 30 hours? Explain. 5. INTEREST A savings account earns 5.23% interest in one year. If the account holds $4,978 for the entire year, about how much will it earn in interest? Explain. 7. CARS Maryanne is saving to buy a car. She wants to have a down payment of 10% for a car that costs $11,783. So far, she has saved $487. If she saves $125 each week for the down payment, how soon can she buy the car? 6. SURVEY In a recent survey, 22% of students at Belletown Middle School participate in music programs at the school. If there are 1,417 students in the school, is 280, 420, or 560 a reasonable estimate for the number of students who participate in music programs? Explain. 8. GAS Lucie s car averages about 34.7 miles per gallon. If a full tank holds 14.3 gallons of gas, about how far can she drive on a full tank of gas? Lesson 5 5 Chapter 5 37 Course 3

29 5-6 NAME DATE PERIOD Lesson Reading Guide Percent and Estimation Get Ready for the Lesson Read the introduction at the top of page 275 in your textbook. Write your answers below. 1. Round the distance from Jupiter to the sun to the nearest hundred million kilometers. 2. Round 19% percent to the nearest ten percent. 3. Use mental math to estimate the distance from Earth to the sun. Read the Lesson 4. What are compatible numbers? 5. Are 1 and 56 compatible numbers? Explain Are 6 and 32 compatible numbers? Explain. 7 Remember What You Learned Describe how to estimate the following using compatible numbers % of out of 59 is what percent Chapter 5 38 Course 3

30 5-6 Study Guide and Intervention Percent and Estimation You can use compatible numbers to estimate a percent of a number. Compatible numbers are two numbers that are easy to divide mentally. Example 1 Estimate 35% of % is about % or and 60 are compatible numbers. 3 Lesson of 60 is So, 35% of 60 is about 20. Example 2 Estimate what percent corresponds to 23 out of or 2 23 is about 24, and 59 is about % 5 So, 23 out of 59 is about 40%. Exercises Estimate % of % of % of % of % of % of 44 Estimate each percent out of out of out of out of out of out of 26 Chapter 5 39 Course 3

31 5-6 Estimate. Skills Practice Percent and Estimation 1. 9% of % of % of % of % of % of % of % of % of % of % of % of 116 Estimate each percent out of out of out of out of out of out of out of out of out of out of out of out of 11 Chapter 5 40 Course 3

32 5-6 Practice Percent and Estimation Estimate % of % of % of % of 35 Lesson % of % of % of % of % of % of % of % of 81 Estimate each percent out of out of out of out of out of out of out of out of ANALYZE TABLES The table gives the land area of one county in each state and the land area of the entire state. Estimate the percent of the land area of each state that is in the county. Then determine which county has the greatest percent of its state s land area. Round to the nearest tenth if necessary. Land Area of Land Area of County County Entire State (square miles) (square miles) Kent County, MD 279 9,774 Marion County, SC ,109 Newport County, RI 104 1,045 Source: U.S. Census Bureau Chapter 5 41 Course 3

33 5-6 Word Problem Practice Percent and Estimation 1. FITNESS At the office where Michael works, 8 out of 17 employees work out at least twice a week. Estimate the percent of employees that work out at least twice a week. 2. PETS Niki asked 25 of her classmates about what pets they have at home. Eleven of the 25 said they had both a cat and a dog. Estimate the percent of Niki s classmates that have both a cat and a dog. 3. BOOKS Jorge has read 19 novels this year, 4 of which were science fiction. Estimate the percent of novels that were science fiction. 4. PARKS The students in Kara s eighth grade science class determined that 9 out of 33 trees at a local park are pine trees. Estimate the percent of pine trees at the park. 5. BAND The marching band at Durango High School has 120 members. Of these, 18% are ninth-grade students. Estimate the number of ninth-grade students in the marching band. 7. HOTELS At the Westward Inn hotel, 48% of the rooms face the courtyard. The hotel has 91 rooms. Estimate the number of rooms that face the courtyard. 6. RESTAURANTS In one east-coast city, 35% of the restaurants in the city are on the bay. The city has 180 restaurants. Estimate the number of restaurants that are on the bay. 8. FARMING Roy has planted soybeans on 68% of his farm this year. Roy s farm has 598 acres of land. Estimate the number of acres of soybeans that Roy has this year. Chapter 5 42 Course 3

34 5-6 NAME DATE PERIOD Enrichment Shaded Regions In these figures, each interior segment bisects, or divides, a region into two equal parts. One-half, or 50% of the circle is shaded, or 25% of the rectangle is shaded, and or 12.5% of the square is shaded. Lesson 5 6 Match the area of the shaded region in each figure with a choice given at the bottom of the page a % b. c. 25% d. e % f. 3 4 g. 50% h. 1 1 i % j. 2 9 k % l. 37.5% Chapter 5 43 Course 3

35 5-7 NAME DATE PERIOD Lesson Reading Guide Algebra: The Percent Equation Get Ready for the Lesson Read the introduction at the top of page 279 in your textbook. Write your answers below. 1. Use a percent proportion to find the area of water in New York. 2. Express the percent for New York as a decimal. Multiply the total area of New York by this decimal. 3. How are the answers for Exercises 1 and 2 related? Read the Lesson 4. What is the percent equation? Write each percent proportion as a percent equation x b p Remember What You Learned 9. Write the percent equation in its three forms. Then choose the best form to find the total price of a jacket after sales tax. Use the sales tax percent for where you live. Find out or estimate to the nearest whole number what you think a jacket will cost where you live. Chapter 5 44 Course 3

36 5-7 Study Guide and Intervention Algebra: The Percent Equation A percent equation is an equivalent form of a percent proportion in which the percent is written as a decimal. part percent whole Example 1 Find 22% of 245. The percent is 22%, and the whole is 245. Let n represent the part. n 0.22(245) Write 22% as the decimal n 53.9 Simplify. So, 22% of 245 is Example is what percent of 750? Lesson 5 7 The part is 600, and the whole is 750. Let n represent the percent. 600 n(750) Write the equation n Divide each side by n Simplify. Since %, 600 is 80% of 750. Example 3 45 is 90% of what number? The part is 45, and the percent is 90%. Let n represent the whole n Write 90% as the decimal n Divide each side by n Simplify. So, 45 is 90% of 50. Exercises Solve each problem using the percent equation. 1. Find 30% of What is 80% of 65? 3. What percent of 56 is 14? is what percent of 40? is 40% of what number? 6. 65% of what number is 78? 7. What percent of 2,000 is 8? is what percent of 4,000? 9. What percent of 3,000 is 18? 10. What is 110% of 80? 11. Find 180% of % of what number is 11? Chapter 5 45 Course 3

37 5-7 Skills Practice Algebra: The Percent Equation Solve each problem using the percent equation. 1. Find 50% of What is 90% of 20? 3. What percent of 64 is 16? is what percent of 30? 5. Find 20% of What is 60% of 45? is 40% of what number? 8. 70% of what number is 63? 9. What percent of 84 is 63? is what percent of 30? is 10% of what number? % of what number is 24? 13. What percent of 2,000 is 4? is what percent of 1,000? 15. What percent of 3,000 is 9? is what percent of 4,000? 17. What percent of 2,000 is 14? 18. What is 120% of 20? 19. What percent of 5,000 is 20? 20. What is 140% of 60? 21. Find 250% of % of what number is 5? 23. Find 175% of % of what number is 21? is 10% of what number? 26. 5% of what number is 20? is 20% of what number? % of what number is 42? Chapter 5 46 Course 3

38 5-7 Practice Algebra: The Percent Equation Solve each problem using a percent equation. 1. Find 80% of What is 30% of 70? 3. What percent of 80 is 32? is what percent of 120? 5. 35% of what number is 84? is 50% of what number? 7. What number is 18% of 72? 8. Find 32% of is what percent of 4,000? 10. What percent of 6,000 is 15? Lesson % of what number is 7? is 10% of what number? 13. Find % of What is 7 1 % of 56? is what percent of 420? % of what number is 44? VIDEO GAMES A video game costs $55. If 7.5% sales tax is added, what is the total cost of the video game? 18. FOOTBALL In the 2006 Super Bowl, Pittsburgh and Seattle each scored 7 points in the 4th quarter. Which team scored the higher percentage of their final score in the 4th quarter? 2006 Super Bowl Team Final Score Pittsburgh 21 Seattle 10 Chapter 5 47 Course 3

39 5-7 Word Problem Practice Algebra: The Percent Equation 1. DINING OUT Trevor and Michelle s restaurant bill comes to $ They are planning to tip the waiter 20%. How much money should they leave for a tip? 2. CHESS The local chess club has 60 members. Twenty-four of the members are younger than twenty. What percent of the members of the chess club are younger than twenty? 3. TENNIS In the city of Bridgeport, 75% of the parks have tennis courts. If 18 parks have tennis courts, how many parks does Bridgeport have altogether? 4. COLLEGE There are 175 students in twelfth grade at Silverado High School. A survey shows that 64% of them are planning to attend college. How many Silverado twelfth grade students are planning to attend college? 5. BASEBALL In a recent season, the Chicago Cubs won 79 out of 162 games. What percent of games did the Cubs win? Round to the nearest tenth if necessary. 7. FOOTBALL In the 2005 season, quarterback Aaron Brooks of the New Orleans Saints had 13 passes intercepted out of 328 attempts. What percent of his passes were intercepted? Round to the nearest tenth if necessary. 6. HOUSING In the Lakeview apartment complex, 35% of the apartments have one bedroom. If there are 63 one bedroom apartments, what is the total number of apartments at Lakeview? 8. SPACE On Mars, an object weighs 38% as much as on Earth. How much would a person who weighs 150 pounds on Earth weigh on Mars? Chapter 5 48 Course 3

40 5-7 NAME DATE PERIOD Enrichment Making Estimates Estimates often vary from person to person. Example Estimate 52% of 1,045. Estimate 1 Estimate 2 52% 50% 52% 1 2 1,045 1,000 1,045 1,050 50% of 1,000 is (1,050) Both estimates are good because both are close to the exact answer, which is Exercises From the list at the right, choose a good estimate for each exercise. Record the letter of your choice in the blank for each exercise and in the box or boxes at the bottom of the page. The message describes something astronomers use estimates for. 1. Estimate 25% of 97. a. 67% b. 10% 2. Estimate the percent for 31 out of 59. c. 600 d Estimate 80% of 62. e. 125% f. 13% 4. Estimate the percent for 6 out of 25. g. 25% h Estimate 48% of 180. i. 25 j. 5% 6. Estimate the percent for 31 out of 42. k. 4 l. 175% 7. Estimate 21% of 39. m. 450 n. 75% 8. Estimate the percent for 4.2 out of 6. o. 80 p Estimate 1 of 238. q. 40% 3 r Estimate 145% of 398. s. 8 t. 50 u. 50% v. 150% w x. 1% y. 225 z. 100% Lesson 5 7 Chapter 5 49 Course 3

41 5-7 Spreadsheet Activity Algebra: The Percent Equation You can use a spreadsheet to solve problems involving the percent equation. Examples Justine goes to the mall looking for bargains. An Angora sweater is on sale for 35% off. The original price of the sweater is $230. Determine the amount she will save on the sweater with the discount. Step 1 Recall that the percent equation states part = percent whole. In this problem, the amount of the discount is the part. Step 2 In cell A1, enter the percent, 35%, and in cell B1, enter the whole, 230. Step 3 In cell C2, enter an equals sign followed by A1*B1. Then press ENTER to return the part or discount. The amount of the discount is $ A B C 35% Sheet 1 Sheet 2 Sheet 3 1. Using the formula from the example above, calculate each of the following. a. 45% of 165 is what number? b. What number is 22% of 120? c. What number is 75% of 300? 2. Write a spreadsheet formula that uses the whole from cell B1 and the part from C1 to calculate the percent. 3. Use the formula from Exercise 2 to calculate each of the following. a. 65 is what percent of 130? b. What percent of 125 is 15? c. What percent of 220 is 11? 4. Write a spreadsheet formula that uses the percent from cell A1 and the part from cell C1 to calculate the whole. 5. Use the formula from Exercise 4 to calculate each of the following. a. 22 is 65% of what number? b. 13 is 50% of what number? c. 50 is 18% of what number? Chapter 5 50 Course 3

42 5-8 NAME DATE PERIOD Lesson Reading Guide Percent of Change Get Ready for the Lesson Read the introduction at the top of page 284 in your textbook. Write your answers below. 1. How much did the price increase from 1963 to 1974? amount of increase 2. Write the ratio. Then write the ratio as a percent. price in How much did the price increase from 1974 to 1978? Write the ratio amount of increase. Then write the ratio as a percent. price in How much did the price increase from 1978 to 1981? Write the ratio amount of increase. Then write the ratio as a percent. price in MAKE A CONJECTURE Why are the amounts of increase the same but the percents are different? Read the Lesson 6. Explain the relationship between selling price and markup. Remember What You Learned 7. When a book has many new terms or ideas, you can sometimes make an outline or concept map to help you understand the information. Read about the new terms on page 284 and the ones just before each example on pages 285 and 286. Then complete the concept map below using these words: discount, more than, new amount, markup, decrease, increase. is less than the original amount percent of Percent of Change is the original amount percent of Lesson 5 8 Example: Example: Chapter 5 51 Course 3

43 5-8 Study Guide and Intervention Percent of Change To find the percent of change, first find the amount of change. Then find the ratio of that amount to the original amount, and write the ratio as a percent. Example Two months ago, the bicycle shop sold 50 bicycles. Last month, 55 bicycles were sold. Find the percent of change. State whether the percent of change is an increase or a decrease. Step 1 Subtract to find the amount of change Step 2 Write a ratio that compares the amount of change to the original number of bicycles. Step 3 Write the ratio as a percent. percent of change amount of change original amount Definition of percent of change 5 The amount of change is 5. The original amount is or 10% Divide. Write as a percent. The percent of change is 10%. Since the new amount is greater than the original, it is a percent of increase. Exercises Find each percent of change. Round to the nearest tenth of a percent if necessary. State whether the percent of change is an increase or a decrease. 1. original: 4 2. original: 10 new: 5 new: original: original: 30 new: 12 new: original: original: 160 new: 63 new: original: original: 96 new: 105 new: 59 Chapter 5 52 Course 3

44 5-8 Skills Practice Percent of Change Find each percent of change. Round to the nearest tenth of a percent if necessary. State whether the percent of change is an increase or a decrease. 1. original: 4 2. original: original: original: 45 new: 6 new: 28 new: 52 new: original: original: original: original: 91 new: 132 new: 105 new: 111 new: 77 Find the selling price for each item given the cost to the store and the markup. 9. suit: $200, 50% markup 10. tire: $50, 40% markup 11. sport bag: $40, 30% markup 12. radio: $120, 25% markup 13. grill: $85, 15% markup 14. microwave: $96, 20% markup Lesson chair: $140, 45% markup 16. camcorder: $350, 33% markup 17. camera: $245, 10% markup 18. diamond ring: $470, 35% markup Find the sale price of each item to the nearest cent. 19. shoes: $70, 10% off 20. artwork: $250, 20% off 21. speakers: $180, 30% off 22. bicycle: $320, 25% off 23. antique chest: $179, 15% off 24. pendant: $93.50, 5% off 25. sofa: $749.95, 35% off 26. oven: $535.99, 20% off 27. guitar: $488.20, 25% off 28. weight machine: $919.70, 10% off Chapter 5 53 Course 3

45 5-8 Practice Percent of Change Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is an increase or a decrease. 1. original: 8 points 2. original: 45 inches 3. original: $60 new: 10 points new: 48 inches new: $48 4. original: $ original: 25 miles 6. original: 12 fouls new: $690 new: 36 miles new: 8 fouls Find the selling price for each item given the cost to the store and the percent of markup. 7. backpack: $14, 40% markup 8. soccer ball: $22, 35% markup 9. music CD: $9, 45% markup 10. sweatshirt: $27, 20% markup Find the sale price of each item to the nearest cent. 11. book: $29, 25% off 12. sofa: $975, 30% off 13. jeans: $34.95, 40% off 14. stereo: $459.99, 15% off Find each percent of change. Round to the nearest tenth if necessary. 15. What is the percent of markup on a $120 cell phone that sells for $149? 16. Find the percent of markup on a $50 pair of shoes that sells for $ Find the percent of discount on a $45 jacket that regularly sells for $ What is the percent of discount on a $290 television that regularly sells for $349? Chapter 5 54 Course 3

46 5-8 Word Problem Practice Percent of Change 1. CLUBS Last year the chess club had 20 members. This year the club has 15 members. Find the percent of change, and state whether the percent of change is an increase or a decrease. 2. READING During Todd s junior year in high school, he read 15 books. In his senior year, he read 18 books. Find the percent of change, and state whether the percent of change is an increase or a decrease. 3. COMPUTERS The computer store pays $250 each for flat screen monitors. The store uses a 30% markup. Find the selling price for each flat screen monitor. 4. SHOES A popular brand of running shoes costs a local store $68 for each pair. Find the selling price for a pair of running shoes if the store has a markup of 75%. Lesson CLOTHING Sandy s Clothing Shop has a markup of 45% on dresses. How much will Sandy s charge for a dress that costs the shop $48? 7. FURNITURE Leta is planning to buy a new sofa as soon as it goes on sale. The regular price for the sofa is $ How much will the sofa cost if it goes on sale for 40% off? Round to the nearest cent. 6. AUDIO The audio store is having a 20% off sale. What will be the sale price on a pair of speakers that normally sell for $280.00? 8. AUTO REPAIR Don is getting a new set of tires for his car. The tires normally sell for $319.96, but they are on sale for 10% off. How much will Don pay for the new tires? Round to the nearest cent. Chapter 5 55 Course 3

47 5-8 NAME DATE PERIOD Enrichment Shady Deals The rectangle at the right has an area of 12 square units. If 75% of the rectangle needs to be shaded, the percent equation can help determine how many units to shade. What number is 75% of 12? n n 9 Shading 9 units would shade 75% of the rectangle. Shade the indicated region of each grid. 1. Shade 75%. 2. Shade 41 2 %. 3. Shade 28%. 3 Shade the indicated region of each grid. If necessary, divide the grid into smaller units. 4. Shade 25%. 5. Shade 22.2%. 6. Shade 18.75%. 7. Shade 62.5%. 8. Shade %. 9. Shade 16.25%. Chapter 5 56 Course 3

48 5-8 NAME DATE PERIOD TI-73 Activity Discounts Suppose you are the owner of a shop that sells casual clothes. Your store often has sales where every item is discounted by the same percent. Use your calculator to find the sales price of each item so that you can have new signs printed that show the sale prices. Example The Moonlight Madness Sale will offer customers 25% off. Find the sale prices. Step 1 Store the amount of the discount in the variable x. Step 2 25 Enter the current price of each item in a list. 2nd % STO ENTER Item Regular [MEM] 6 ENTER Price 1 Cotton Sweater Denim Jacket Team Sweatshirt Sport Socks 3-Pack T-Shirt 7.99 Step 3 LIST In L1 enter each regular price. Press after each price. Enter a formula in L2 to calculate the sale price. sale price regular price (discount %)(regular price) 2nd [STAT] 1 ENTER [STAT] 1 2nd 2nd [TEXT] Done x [TEXT] Done ENTER The sale price for each item is displayed in L2. Use the list of data to answer the questions below. 1. List the sale prices for the Moonlight Madness Sale. 2. Explain why the formula for L2 correctly calculates the sale price. 2nd Lesson Use the same lists L1 and L2 to find sale prices when the discount rate is 35%. (Hint: Store a new value in x.) 4. Add a new item: a suede jacket priced at $ What is its sale price when the discount is 35%? 5. Create a new list, L3, to find the amount of the discount for each item at 35% off. Chapter 5 57 Course 3