Chapter 6. Section 6.1. Chapter 6 Opener. Big Ideas Math Red Worked-Out Solutions. 6.1 Activity (pp ) Try It Yourself (p.

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1 Chapter 6 Opener Try It Yourself (p. ) 6. 6% % % % 7 %, or %, or 5 5%, or % 5 5 Section Activity (pp. 5). a. b. d. f.. a. b. c. d. %. % c. 7 7%.7 e. 5 5%.5 g %.5 %. 6 6%.6 6 6% %.5...% %.5. a... % % % % % b. One Tenth Ten Hundredths Ten Percent. % % % % Twenty-four Hundredths Twenty-four Percent 5 c..5 5% 6. % Fifty-eight Hundredths Fifty-eight Percent 65

2 Chapter 6 d..5 5 Five Hundredths 5% Five Percent 6... % Check: % Check:. When you rewrite ercent as a decimal, move the decimal point places to the left. When you rewrite a decimal as ercent, move the decimal point places to the right. 5. Sample answer: Because you are multiplying and dividing by powers of % Check: 6. On Your Own (pp. 6 7). %.%. Check: % 9. out of %.%. Check:. Water:. 5 Sand:.5. 7% 7.%.7 Check: Water reflects 5.6 times more UV rays than sand. 6. Exercises (pp. 9). 9.7% 9.7%.97 Check: Vocabulary and Concept Check. B;.. %. D;.. %. C;...% % Check:. A;...% 5. Sample answer: %.%. %.%. Three decimals that are between % and % are.,., and.9. 66

3 Chapter % %.7.7 7% So, after converting to percents,.7 does not belong because it represents 7% instead of 7%. Practice and Problem Solving 7. 7% 7.%.7. 6% 6.%.6 So,.6 of the songs on your MP player are pop songs.... % About % of the length of a cat is its tail.. 9% 9.%.9 So,.9 of the computer s capacity is free space % 6.%.6. 55% 55.% %.5% %.5% % 57.%.57. %.%.. 9% 9.% % 6.%.6. a. Car: %.%. School bus: %.%.. 7.6% 7.6% % 9.5%.95 Bicycle: %.%. b. Car: % % 66.%.66 5 School bus: %. 6. 7% 7.% %.6%.6..%.%. Bicycle: %. 5 5 c. % ( % + % + %) % 76% % % So, % of students use another method to travel to school % % d. Answer should include, but is not limited to: A bar graph showing either the number of students or the portion of students in the class that get to school in various ways % % % % 9. % 6% % So, the other candidate received % of the votes.. a. Blue: % Red:.6.6 6% 6....% Yellow:.. % % % % %. The decimal point was moved in the wrong direction % 6, 5 % + 6% + % 7% So, 7% said red, blue, or yellow. b So, 6.5 times more students said red than yellow. 67

4 c. Method : Use percents. % ( % + % + 6% + % ) % % 6% So, 6% of the students said green. Method : Use decimals. ( )..6 6% So, 6% of the students said green. Sample answer: Method is preferable because it is easier to work with whole numbers and there are fewer steps.. a % 6.6% So, 6.6%, or 6 %, of the MVPs were running backs. b..6 were running backs. Then, were not running backs So, 5 6 Fair Game Review.. 5. of the MVPs were not running backs x + 9x x + + ( 9x) x + ( 9x) + + ( ) x + 9 5x n 6.n 5 +.n + ( 6) + (.n).n + (.n) ( 6). + (.) n ( 6).6n. y 5( y ) y + ( 5) y ( 5)( ) + ( 5) y ( 5) y + 5 b + + b b + () + b b + + b b + b + ( + ) b + b 9. ( ) ( ) 5. B; So, you pay $.95 more for the ham. Section Activity (pp. ). a. Using ercent to represent a sales tax rate is more common. 7% 7.% Because.7 >.5, 7% sales tax is greater than sales tax. b. Using a fraction to represent an ingredient amount is more common Because.7 >.,.7 cup of flour is greater than cup of flour. c. Using a fraction to represent a wrench measurement is more common Because 5 >, the 5 -inch wrench is larger than the.75-inch wrench. 6

5 d. Using a decimal to represent a money amount is more common Because.6 >.56, 5 dollars is greater than.56 dollars. e. Using ercent to represent a test score is more common. 9% 9.% Because.9 >.75, the 9% test score is greater than the 7 test score. f. Using a decimal to represent the volume of roduct is more common Because 5. > 5.6, the 5 -fluid ounce tube is 6 greater than the 5.6-fluid ounce tube.. Sample answer: a. Write them all as decimals..5 b %.% %.%. 7% 7.% So, you need to order.5,.,.5,.7,.,.,.7,.7, and...7 The numbers from least to greatest are 7%, %,,,.7,., %,.7, and Answer should include, but is not limited to: The cards are made correctly. The game is played according to the rules. On each play, the numbers on the cards are compared correctly to determine the winner.. Sample answer: To order numbers that are written as fractions, decimals, and percents, convert all the numbers to percents and then order the percents. Example:.5, 6%,, % % % The percents in order from least to greatest are 6%, 5%, 7%, and 75%. The numbers in order from least to greatest are 6%,.5,.7, and

6 5. nickel; The name nickel comes from the metal the coin was originally made from; cent ; dime comes from the French word disme meaning tenth-part; quarter dollar; half dollar dollar. 6. On Your Own (pp. ). 7 7 % 5 5 5% is less than %. So, 7 5 is the greater number.. 9% 9.%.9.9 is less than.9. So, 9% is the greater number.. You: 75% 75.%.75 Sister: Exercises (pp. 5) Vocabulary and Concept Check. Fraction Decimal Percent %.5 5%.6 6%.6 6%.5 5% Friend:.7 You: 75%.75 Sister:.65. Sample answer: Write 5 as ercent, then compare it to is the greatest number. So, you made the most shots.. Texas:. % 5 Illinois:..% Ohio % Illinois Michigan.% % % % % 6% % % % % Washington % New York 6% Texas % California % The states in order from least to greatest are Washington, Michigan, Ohio, Illinois, New York, Texas, and California. 59% to determine which is greater...;. %, but %,, 5 to %. and. are all equal Practice and Problem Solving..9 9% 9% is less than 95%. So, 95% is the greater number. 5. %.%.. is greater than.. So, % is the greater number % 5 5 7% is greater than 7%. So, 7 5 is the greater number % 5 5 5% is less than 5%. So, is the greater number. 5. 6% 6.%.6.6 is less than.6. So, 6% is the greater number % 76.% is greater than.67. So, 76% is the greater number. 7

7 % 6% is less than 6.5%. So, 5 is the greater number... % % is greater than.%. So,. is the greater number.. 6 6% 5 5 l7% is greater than 6%. So, 7% is the greater number.. %.%.. is greater than.. So, % is the greater number %.% is greater than %. So, is the greater number % 9 % is greater than 77.7%. So, % is the greater number. 6. %.% The numbers in order from least to greatest are, %, and % 6.% The numbers in order from least to greatest are.6,, and 6%.. 6 6% % % %... 5 % % 5 6%.6.9 9% 7 7.5% % 6% % 9% The numbers in order from least to greatest are %,, 5 7, and % %.5%.5.5% 5% % 5% % 5% The numbers in order from least to greatest are.5%,.5, and. 7

8 % 6.%.6 7% 7.%.7 6.%.6 The numbers in order from least to greatest are 6.%,.6,,.6, and 7% % %.7% % The numbers in order from least to greatest are 7,,.7%, and.. 5. % 5 5 yes; % is greater than %. So, you reached your goal.. Brazil:.%.% India: Russia:. 5 5 Russia. 5 United States. The countries, by population, in order from least to greatest are Russia, Brazil, United States, and India % % 66 % % The numbers in order from least to greatest are.66, 66.%,, and Brazil.%. 66 % %.66 66% 66% 66.5% 67% 66.% India

9 % % % % 9 % 5 5 The numbers in order from least to greatest are %,.,, 5 and A;. 5 5 A is at.. 7. D; 5.% 5.%.5 D is at.5.. B; B is at C;. % 9 % % % % C is at.. 5 % 9 9%. Stage : Stage :. 5 5 Stage : %.%. Stage :. Stage :. Stage 7: Stage 7:. The stages from shortest to longest are Stage, Stage 7, Stage, Stage, and Stage 7.. a. Dolphin:...%.75 9 Rabbit: % 6 Squirrel: 6 6% 5 5 The animals, by sleep time, in order from least to greatest are dolphin, rabbit, lion, squirrel, and tiger. b. Sample answer: I sleep hours a day, or Rewrite Stage :.55 Dolphin:.% Tiger: 65.% Lion: 56.% % 5% 5% 55% 6% 65% 7% Rabbit: 7.5% Squirrel: 6% as ercent...%. 9 9 of a day. I sleep.% of the day. c. Sample answer: My sleep portion is the least. 7

10 . a. a 7; The smallest value of a for which % a < is % a a % % So, the numbers are ordered from least to greatest when a 7. b. There is none; For to be less than %, the value of a a must be greater than, but when this is true, a is greater than %. Fair Game Review % % % 9% % % % % % The ratios are equivalent. So, 6 and 9 5 form a proportion is in simplest form. 6 7 The ratios are not equivalent. So, 7 6 roportion The ratios are equivalent. So, proportion. 6. D; n > + + n > n > n > Section Activity (pp. 6 7). a. % So, from the model, 5 is 5% of. b. % 5% 7.5 5% 5 5% 5 and do not form and 5 form a So, from the model,.5 is 75% of. c. % % So, from the model, is % of. d. 5% %.5 % 6 6% 75%.5 % % % % % % % % 5% 6% 7% % 9% % So, from the model, 6% of is about.5. e. % % 66 % % So, from the model, 65% of is about. 7

11 Chapter 6. a. % % % 6% % % b. Sample answer: So, from the model, 5 is % of 75. b. % 5% 5% 75% % 5 5 Part Whole So, from the model, 5 is 5% of. c. % 5% % c. Sample answer: So, from the model, 5 is 6.5% of. e. % 5% % 5% % d. %.5% 5% 7.5% 5% 6.5% 75% 7.5% % 9.5 is close to the estimate of. So, the estimate is close to the exact answer. So, from the model, is about 5% of. Part 9 5 Whole 5 5 is close to the estimate of 5%. So, the estimate is close to the exact answer. So, from the model, 75 is 5% of 5.. a. % % 66 % % 7 d. Sample answer: 5 So, from the model, is % of 7. b. % 5% 5% 75% % Whole Sample answer: To use a model to estimate percent % % 6% % % 55 questions, let the length of the model represent the whole, then shade the model to represent the part of the whole and determine the percent. So, from the model, is % of 55. d. % Part is equal to the estimate from the model. So, from the model, is 5% of 5. c. % 9 5% 5% 75% % % 5% % So, from the model, 75 is 75% of. From this model, is 5% of 6. 5% e. % 5% 5% 75% % 6 % % % % % 5% 6% 7% % 9% % From this model, 6 is 75% of. So, from the model, is 5% of.. a. Sample answer: Part Whole 6. part percent whole is close to the estimate of.5. So, the estimate is close to the exact answer. 75

12 6. On Your Own (pp. 9).. p 5 p 5 p 5 p 5 6 p 5 p So, 6% of 5 is. So, 5 is 5% of. a 6 a a So, is % of 6. a.5 a a.5 So, % of.5 is.5.. w w So,.% of is. So, a 5 a 5 5 a a w 5 5w w is 5% of. So, 9 of the 5 tornadoes occurred in central Alabama. 6. Exercises (pp. ) Vocabulary and Concept Check. The percent proportion is where a is part of p the whole w, and p%, or, is the percent... % is and the number w is the whole. Set up the percent proportion as a 6 a 5 a 5 a So, 6% of is. a w and solve for a.. ; 5 n This proportion is not ercent proportion. The other three are percent proportions. Practice and Problem Solving 5. % 9. is close to the estimate of. So, % of is about. 6. % 5% 5% Part. 9. Whole % 5 5% 7 % 5 75% 5 7.5% is equal to the estimate on the model. So, 5 is 7 %, or 7.5%, of. 6 % 5% 6 % 75% 7 % % Part Whole

13 7.. % is equal to the estimate on the model. So, 5 is % of is equal to the estimate on the model. So, is % of % % is close to the estimate 7 %, or 7.5%, of 5.. % % % % % 5% 6% 7% % 9% % Part 5 Whole 5 % % % 6% % Part Whole 7 % 6.5 5% Part 7 % %. % % % 6 % 75% 7 % % 6 Whole 5 5% So, is about 6 6 Part 75 Whole 6 5% 75% % is equal to the estimate on the model. So, is 75% of p 5 p 5 p So, % of 5 is. p 56 p p 5 p So, is 5% of w 9 w 6 w So, 5% of 6 is w 6, 9w w So, 6 is.9% of. a 75 a a a 9 So, 75% of is 9. 77

14 a 9 a 9 a a 99 So, % of 9 is 99. a. a a 6 a a.6 So,.6 is.% of. 7 p 5 p 5 p 5 6 p So, 7 is 6% of The value of is in the wrong position. w 5 5 w 7 w 5 w So, % of 5 is..... a 5 a a a So, there were students who earned the Presidential Physical Fitness Award. w, w 6 w So, the amount of sales is $6..5 p.5 p.5 p So,.5 is.5% of w, 55w w So,. is 5.5% of. 7

15 . 6 6 w 75 6w 75 6w w So, is 6% of 5, or. 5. a a a 7 5 a 7 a 7 6. So, 7 is 5% of 7. a 7.5 a 75 a 7 a 7 a You completed math exercises before dinner, so you have left to complete after dinner w 5 5w. w So, last year your friend earned $. per hour There were campsite reservations last week of them were for Friday and Saturday. 56 p p p p 66 p So, 66 % of the reservations were for Friday and Saturday. 9. a. The scale on the vertical axis is missing. b. Greg has the shortest bar, with out of 6 parts. p 6 p p p p 6.5 p So, Greg has 6.5% of the votes. c. Chloe has out of 6 parts, or of the votes. 6 So, she received votes. 79

16 . Assume x >. x x w 5x w So, % of the number would be 5x.. a. Assume x >. 5x p x 5 p 5 p 5 p 6.5 p So, 6.5% of x is 5x. b. Assume x >. a 65 x a x a x x x a 5x So, 65% of x is 5x. Fair Game Review a b 5 5. ( ) ( ).. ( ) b a ( ) ( )( ) b a B; 9x. 9x. 9 9 x. Section Activity (pp. ). a. Candidate Sue Miguel Leon Hong b. Sue: 5%, Miguel: 5%, Leon: %, Hong: % Sample answers: Using the percent proportion for Sue: Set up ercent proportion and use the Cross Products Property to solve the proportion. p p 5 p Using division for Miguel: Divide the part by the whole in simplified form to find the percent % Using a ratio table for Leon: Use a ratio table to find the part when the whole is. 5 Part Whole 6 Number of votes received Total number of votes 5 5, or 6 9, or 6, or 6 5, or 6 5 Using a ratio table for Hong: Use a ratio table to find the part when the whole is. 5 Part Whole 6 5

17 c. Check students work. Sample answer: Dividing the part by the whole is the most efficient method.. a. Sue: votes, Miguel: votes, Leon: votes, Hong: votes Sample answers: There are 6 students who voted. Using ercent proportion for Sue: Set up roportion and use the Cross Products Property to solve the proportion. a a a a a Using a ratio table for Miguel: Use a ratio table to find the part when the whole is. 5 6 Part Whole 5 6 Using a ratio table for Leon: Use a ratio table to find the part when the whole is. 5 6 Part 5 7 Whole 5 6 Using a decimal for Hong: Change the percent to a decimal and multiply by the total number of students,..5 b. Check students work. Sample answer: Changing the percents to decimals and multiplying by the total number of students is the most efficient method.. a. part percent Definition of percent whole part Multiply each side by whole percent whole whole the whole. Divide out common part percent whole factors. This is the percent equation. b. Sue: part percent whole. Miguel: part percent whole. Leon: part percent whole.5 Hong: part percent whole.5 Sample answer: The percent equation is more efficient because rewriting the given percents as decimals or fractions and multiplying by the whole is quicker to perform than setting up roportion, multiplying each side by a number and solving, or using cross products to solve.. a. a.55 b Sample answer: Solve ercent problem by using the percent equation a p w, where p is a decimal or fraction. 6. Percent proportion: 6 p 5 Percent equation: 6 p 5 6. On Your Own (pp. 5). a p w. So, is % of.. a p w.5 6 So, 6 is 5% of.. a p w. a p w p 6 p p 6 p p.9 p Because.5 equals Because.9 equals.5%, is.5% of 6. 9%, is 9% of. 5. a p w 6. a p w. w 9. w. w 9. w.... w 5 w So, is % of. So, 9 is % of 5. w

18 7. a p w So, the amount of the tip is $ Exercises (pp. 6 7) Vocabulary and Concept Check. Percent equation: a is p percent of w. The part of the whole is equal to ercent times the whole.. n is greater than m because the percent is greater than %. Because 5%.5, n.5 m.. The question 55 is % of what number? is different because it represents the equation 55. w, whereas the other three questions represent the equation a w 55. w.. 75 w So, 55 is % of 75. a 55 So, is % of 55. Practice and Problem Solving. Convert the percent to a decimal and multiply it by. a p w a a. 9. So, 9. is % of. 5. Divide 5 by and write the quotient as a decimal. Then convert the decimal to ercent. a p w 5 p 5 p p % p p So, 5 is 7.5% of. 6. Convert % to a fraction and reduce it. Then multiply 5 by the reciprocal of the fraction to find the number. a p w 5 w 5 w 5 w 5 w 5 w So, 5 is % of Convert the percent to a decimal and multiply it by 7. a p w a a. 7 So, is % of 7.. Use the percent proportion and write the percent as a mixed number. p 5 5 p 5 p 5 p 6 p 6 So, is %, or about.5%, of Convert 75% to a fraction and reduce it. Then multiply by the reciprocal of the fraction to find the number. a p w 75 w w w 6 w 6 w So, is 75% of 6.

19 . a p w. 5 So, % of 5 is.. a p w. a p w 5 p w 5 p w p w Because.75 equals So, 5% of is 5. 75%, 5 is 75% of 6.. a p w. 5. So,.% of 5 is... a p w 5. a p w 9 p.5 w 9 p.5 w p w Because.5 equals So,.5% of is. 5%, 9 is 5% of. 6. a p w 7. a p w 5 p. w 5 p. w...7 p 5 w Because.7 equals So, % of 5 is. 7%, 7% of is 5.. You need to convert the percent to a fraction or decimal before using the percent equation. a p w.5 7 So, 7 is 5% of. 9. The number represents the part of the whole, not the whole. a p w.6 w.6 w w So, is 6% of 5.. Answer the question: What is.5% of $? a p w.5 The salesman receives $ in commission.. Answer the question: $675 is 5% of what dollar amount? a p w w w w The goal was $5.. Answer the question: $ is what percent of $? a p w p p.5 p Because.5 equals 5%, the percent of sales tax is 5%.. a p w 5 x 6 Rutledge s age was 6.. a p w 7. y 7. y.. 7 y Franklin s age was From Exercise, y 7. a p w n y 7 56 There were 56 signers. 6. y is what percent of ( n + y x)? From Exercises 5, you know that x 6, y 7, and n 56. a p w y p ( n + y x) 7 p ( ) 7 p 7 p.7 p Because.7 equals 7%, y is 7% of ( n + y x).

20 7. If the percent is less than %, the percent of a number is less than the number. For example, 5% of is. a p w.5 If the percent is equal to %, the percent of a number will equal the number. For example, % of is. a p w If the percent is greater than %, the percent of a number is greater than the number. For example, 5% of is. a p w.5. a. Percent representing other Percent Percent % representing + representing baseball football % (.% + 7.5% ) % 77.5%.5% Answer the question: is.5% of what number? a p w.5 w.5 w.5.5 w So, students participated. b. Answer the question: What number is 7.5% of? a p w.75 So, students chose football. 9. a. Answer the question: What number is 66% of 55 gallons? a p w There are 6 gallons of water in tank A. b. Set up roportion using the fact that the ratio of the capacity of tank A to tank B is :5. capacity of tank A capacity of tank B 5 55 capacity of tank B 5 Capacity of tank B The capacity of tank B is 75 gallons. c. Answer the question: What number is 5% of 75 gallons? a p w There are 97.5 gallons of water in tank B.. false; For example, 5 is 5% of 6. So, 6:5 : but 75 : 5 :.. First find the points earned on each test. What number is % of? a p w. points were earned on the first test. What number is 9.6% of 5? a p w points were earned on the second test. What number is % of 5? a p w. 5 points were earned on the third test. Now find 9% of the total of all the tests. The total points for all four tests is a p w.9 7 So, you must earn 7 total points to earn a 9%. Now find how many points are needed on the last test. Points needed on last test 7 ( ) 7 76 To find the test score needed on the last exam to earn 9% of the total points, answer the question: 76 is what percent of? a p w 76 p 76 p.9 p Because.9 equals 9%, a test score of 9% is needed on the last exam to earn 9% of the total points. Fair Game Review A; boys x total 6

21 Study Help Available at BigIdeasMath.com. Quiz %.%...%.%.. 6.5% 6.5% % % % % 7.%.7.7 is greater than.7. So, 7% is the greater number.. %.%.. is less than.. So,. is the greater number. 9. 5% 5.% %.5.. The numbers in order from least to greatest are 6, 5., and 5%.. %.% %.... The numbers in order from least to greatest are 7 %,, and.. 6 p 5 p 5 p 5 p So, % of 5 is 6. 5 p 5 7 p 5 7 p 5 p So, 5 is % of 5. 5

22 .. a 5 a 5 5 a a So, is % of w 5 5w w So,.5% of is a p w. 75 So, is % of a p w. w.w.. w So, is % of. 7. %.%. So,. of the fish caught are perch.. Team : % 5 Team :.. % Team : 77.5% Team :.5.5.5%.75 9 Team 5: % Team 6: 76.5% Team 7: % Team :.5% Team 6: 76.5% Team :.5% Team : 77.5% Team 5: 7.5% Team : % 7% 7% 7% 76% 7% % % % Team : 75% Team 7: 7.75% Team :.5%.5 is the greatest number. So, Team collected the most items. 9 is the least number. So, Team 5 collected the fewest items. 9. Answer the question: What number is 6% of 5? a 6 5 a a 7 So, the quarterback completed 7 passes. 6

23 Population Chapter 6. Answer the question: is % of what number? a p w. w.w.. 5 w So, your cell phone can hold 5 messages. Section Activity (pp. ). a. % of % of % of % of % of % of Dam Salmon Dam Salmon a. % of,., 6, + 6,6 % of,6.,6 67,6 + 67,77 % of,77.,77 75, , % of 9,. 9, 9, + 9, % of 9,. 9, 9 9, + 9 9,7 % of 9,7. 9,7 97 9,7 + 97,7 % of,7.,7 5,7 + 5,676 Year Population,,6 b. Number of Salmon 6 Surviving Salmon Dams c. The number of young salmon decreases by % % % with each dam. 5,77 6 9, 7 9, 9,7 9,7,676 6,,,,, 6,,,,, 6,,, Population of a City Year 9 7

24 Population Chapter 6 b. % of,., 5, + 5,5 % of,5.,5 556, ,96 % of 9,96. 9, , ,669 % of 9,669. 9, , ,59 % of,59.,59 6,59 + 6,67 % of,67.,67 66, ,9 % of,9.,9 65,9 + 65, Year Population,,5 5 9,96 6 9,669 7,59,67 9,9, Population of a City 6,,,,, 6,,,,, 6,,, Year 9 c. The organization in part (b) projects the larger population by,,676 6 people.. A percent of decrease is the percent a quantity decreases from the. A percent of increase is the percent a quantity increases from the.. Sample answer: You can use ercent of decrease to represent the discount of an item that is on sale at a grocery store. You can use ercent of increase to represent the increase in the salary of an accountant after a raise. 6.5 On Your Own (pp. ). The number of inches increases, so the percent of change is ercent of increase. new amount percent of increase 5 5.5, or 5% So, the number of inches increased 5%.. The number of people increases, so the percent of change is ercent of increase. new amount percent of increase , or about.% So, the number of people increased about %.. The number of home runs decreased from to. So, the percent of change is ercent of decrease. new amount percent of decrease., or about.% So, the number of home runs decreased about.%.. The amount of error is feet. amount of error percent error actual amount.95, or about 9.5% You have the greater percent error. Your percent error is about.% and your friend s percent error is about 9.5%.

25 6.5 Exercises (pp. 5) Vocabulary and Concept Check. When the increases, the percent of change is called ercent of increase. When the original amount decreases, the percent of change is called a percent of decrease.. The 5 bonus points on a 5-point exam has a greater 5 percent of increase because 5 is less than, so 5 5 is greater than.. A % decrease means the quantity decreased to. Practice and Problem Solving. Amount of increase: 5% of.5 The increase is meters. So, the new amount is + meters. 5. Amount of increase: 6% of The increase is 9 liters. So, the new amount is liters. 6. Amount of decrease: 6% of The decrease is points. So, the new amount is 5 7 points. 7. Amount of decrease: % of 5. 5 The decrease is penalties. So, the new amount is 5 7 penalties.. The number of inches increases, so the percent of change is ercent of increase. new amount percent of increase 6, or % So, the number of inches increased %. 9. The number of people decreases, so the percent of change is ercent of decrease. new amount percent of decrease , or about 66.7% So, the number of people decreased about 66.7%.. The number of pounds decreased, so the percent of change is ercent of decrease. new amount percent of decrease , or % So, the number of pounds decreased %.. The number of songs increased, so the percent of change is ercent of increase. new amount percent of increase 7 5.5, or 5% So, the number of songs increased 5%.. The number of gallons increased, so the percent of change is ercent of increase. new amount percent of increase., or % So, the number of gallons increased %.. The number of paper clips decreased, so the percent of change is ercent of decrease. new amount percent of decrease , or.5% So, the number of paper clips decreased.5%. 9

26 . The number of centimeters increased, so the percent of change is ercent of increase. new amount percent of increase , or about 76.% So, the number of centimeters increased about 76.%. 5. The number of miles decreased, so the percent of change is ercent of decrease. new amount percent of decrease , or 7.5% So, the number of miles decreased 7.5%. 6. The denominator of the fraction should be the original amount,. new amount percent of increase 6., or about % 7. The number of minutes decreases, so the percent of change is ercent of decrease. new amount percent of decrease.5, or.5% So, the number of minutes it took you to finish Level decreased.5%. 9. a. The amount of error is. amount of error percent error actual amount 6.67, or about 6.7% The percent error is about 6.7%. b. To get the same percent error, the amount of error needs to be the same. Because your estimate was people below the actual attendance, an estimate of people above the actual attendance will give the same percent error. So, the other estimate that gives the same percent error is + people.. The quantity increases. So, the percent of change is a percent of increase. new amount percent of increase or % So, the quantity increased %.. The amount of error is 6. amount of error percent error actual amount 6.5, or 5% The percent error is 5%. 9

27 . The quantity decreases. So, the percent of change is a percent of decrease. new amount percent of decrease , or 5% So, the quantity decreased 5%.. The quantity increases. So, the percent of change is a percent of increase. new amount percent of increase 7., or about.% So, the quantity increased about.%.. The quantity decreases. So, the percent of change is a percent of decrease. new amount percent of decrease , or 7% So, the quantity decreases 7%.. A change from to is a % increase because the increases by the. A change from to is a 5% decrease because the decreases by half the. 5. a. The population increases from 7 to. So, the percent of change is ercent of increase. percent of increase new amount,,,,,.695, or about 6.95% So, the population increased about 6.95%. b. Amount of increase: 6.95% of,.695,,9 The population will increase from to 9 by,9. So, the population in 9 will be, +,9 6,9. 9

28 6. a. Original perimeter: P 7. + w ft ( ) ( ) New perimeter after dimensions are doubled: P + w ( ) + ( 6) ( ) + ( ) + 6 ft The perimeter increases. So, the percent of change is a percent of increase. new amount percent of increase 6, or % So, the perimeter increased %. A w 6 6 ft b. Original area: ( ) New area after dimensions are doubled: A w 6 ft ( )( ) ( )( ) The area increases. So, the percent of change is a percent of increase. new amount percent of increase 6 6 6, or % So, the area increased %. amount of error percent error actual amount amount of error.5 6 amount of error amount of error The least acceptable weight is ounces. The greatest acceptable weight is ounces.. The time decreases. So, the percent of change is ercent of decrease. Convert the times to decimals. 5 7min5sec 7 + min 6 ( ) min 7.75 min 5 5min5sec 5 + min 6 ( 5 +.5) min 5.5 min new amount percent of decrease , or about.5% So, the time decreased about.5%. 9. less than; Sample answer: Let x represent the number. A % increase is equal to x +. x, or. x. A % decrease of this new number is equal to.x.(. x), or.99x. Because.99 x < x, the result is less than the original number.. Let x last year s donation. x +.5x,.5x,.5.5 x $ Let y donation from two years ago. y +.y.y.. y $ So, $ was raised two years ago. 9

29 . Number of girls in science club: 5% of.5 Let x be the number of new girls that join the club. percent of girls in club current number of girls + number of new girls current number of members + number of new girls + x.56 + x.56( + x) + x.56( ) +.56( x) + x. +.56x + x. +.56x.56x + x.56x. +.x. +.x..x..x.. x So, new girls joined the club. Fair Game Review. a p w So, 6 is 5% of 6.. a p w 9. p 9. p.5 p Because.5 equals 5%, 9. is 5% of.. a p w 5. a p w 5.5 w. w 5.5w. w w 56.5 w So, 5 is 5% of. So, is % of B; For A: is in simplest form The ratios are equivalent. So, and 6 form a proportion. For B: is in simplest form. 7 7 is in simplest form. The ratios are not equivalent. So, 7 and 7 do not form roportion. For C: 6 6 is in simplest form. The ratios are equivalent. So, 6 and form a proportion. For D: is in simplest form. The ratios are equivalent. So, 6 and 5 form a proportion. Section Activity (pp. 6 7). a. % % % $ $9 $ $7 $6 discount $ sale price $5 $ $7 $5 b. % 5% % $ $9. $9.6 $9. $9. $.5 discount $.5 sale price $9 $.5 $.5 $9 9

30 c. % 7% %. a. % 5% $ $7. $5.6 $. $. $7. discount $7. sale price $9 $7. $.7 Store C is the best buy if you get the full 7% off because it is the least expensive sale price. $9 $ $5 $.5 increase in price 5% of selling price $56.5 Selling Price $56.5. a. Original: % $x b. % 5% $ $. Original Price Original: 7% $. percent dollars 7 7%. 7 %. % So, the original price is $. b. The sale price is % % 7% of the original price. Answer the question:. is 7% of what number? w 7w w So, the original price is $. c. $ $5 $6.5 increase in price 5% of selling price $.5 % 5% $ $7 $.5 increase in price 5% of selling price $.5 Selling Price $.5 Selling Price $.5. Sample answer: To find discounts, use the percent of the discount to set up and divide a model into sections. For example, to find a discount of 5% on $5, divide a model into sections of 5%. That way, you can find the amount of the discount and the price. To find markups, use the percent of the markup to set up and divide a model into sections. For example, to find a markup of 5% on $, shade sections on a model to represent %, or $. Then add sections to represent the markup of 5%. Use the model to find the price. 6.6 On Your Own (pp. 9). The discount is % of $5. a p w. 5 sale price original price discount 5 So, the sale price is $.. The sale price is % 5% 5% of the original price. Answer the question: is 5% of what number? a p w.5 w w So, the original price of the DVD is $. 9

31 . The markup is % of $75. a p w selling price cost to store + markup So, the selling price of the aquarium is $ Exercises (pp. 5 5) Vocabulary and Concept Check. Sample answer: To find the sale price of an item that has been discounted 5%, multiply the original price by % 5% 75%.. To find the selling price of an item that has been marked up %, first find the amount of the markup by finding % of the cost to the store. Then find the selling price by adding the amount of the markup to the cost to the store.. a. Because a discounted price is less than the original price, the 6% tax will be less on the discounted price. So, it s better to pay 6% tax on a discounted price. b. A $ markup on a $ shirt is the same as a % markup on a shirt. Because % < %, it s better to pay % markup on a $ shirt. Practice and Problem Solving. The discount is % of $. a p w. 6 sale price original price discount 6 6 So, the sale price is $6. 5. The discount is 5% of $. a p w.5 6. sale price original price discount So, the sale price is $ The discount is % of $. a p w. 96 sale price original discount 96 So, the sale price is $. 7. The discount is % of $. a p w. 5. sale price original discount So, the sale price is $ The discount is 6% of $69.. a p w sale price original discount So, the sale price is $ The sale price is % 5% 75% of the original price. Answer the question: is 75% of what number? a p w.75 w 5. w So, the original price is $5... The sale price is % 5% 95% of the original price. Answer the question: 57 is 95% of what number? a p w w 6 w So, the original price is $6.. The sale price is % % % of the original price. Answer the question: 9 is % of what number? a p w 9. w 5 w So, the original price is $5.. The sale price is % 6% 6% of the original price. Answer the question: 7 is 6% of what number? a p w 7.6 w w So, the original price is $.. The sale price is % 5% 5% of the original price. Answer the question: 6.5 is 5% of what number? w 7. w So, the original price is $7.. 95

32 original price sale price percent of discount original price , or 5% So, the percent of discount is 5%. percent of discount original price sale price original price , or % So, the percent of discount is %. percent of discount original price sale price original price , or 5% So, the percent of discount is 5%. Table for 6 Original Price Percent of Discount $ % $6 Sale Price $ 5% $5.7 $ % $ $ % $76.6 $69. 6% $ The markup is % of $5. a p w. 5 5 selling price cost to store + markup So, the selling price is $55.. The markup is 6% of $. a p w.6 selling price cost to store + markup + So, the selling price is $. 9. The markup is 5% of $. a p w.5 5 selling price cost to store + markup So, the selling price is $75.. Your classmate is not correct. To find the percent of markup, you need to find the percent of increase. selling price cost percent of increase cost , or 75% So, the percent of markup is 75%.. To find the sale price, either multiply $5.5 by. or multiply $5.5 by.9, then subtract from $5.5. Using the method of multiplying $5.5 by. only involves one step, so that method is preferable. $5. 5% $ $6 5% $57 $5 % $9 $ 6% $7 $7. 5% $6.5 $6 5% $5 $ % $65.6 $95 5% $

33 . a. Store A: The markup is % of $6. a p w selling price cost to store + markup So, the video game system sells for $6. at Store A. Store B: The markup is % of $55. a p w selling price cost to store + markup So, the video game system sells for $.5 at Store B. Store C: the markup is 5% of $6. a p w.5 6 selling price cost to store + markup 6 + So, the video game system sells for $ at Store C. You should buy the system at Store C because it sells the system for less than the other two stores. b. percent of discount Store A price Store C price Store A price , or about.% So, Store A must offer at least an.% discount.. The stereo is not free. The first discount is % of $9.5. a p w sale price original price discount The second discount is 6% of $77.7. a p w sale price original price discount So, after both discounts, the sale price is $.. In order for the stereo to be free, or cost $, the second discount must be %, not 6%.. a. percent of discount original price sale price original price , or about 5% So, the percent of discount is about 5%. b. Answer the question:.95 is what percent of 9.99? a p w.95 p p Because.65 equals 6.5%, the percent of sales tax is about 6.5%. c. percent of markup selling price cost cost x x.6x 9.99 x.6x x So, the cost of the jeans to the store is $.99. selling price cost percent of markup cost , or about % After the discount, the percent of markup is about %. 5. First find the discounted price before the sales tax. percent of increase (sales tax) amount with sales tax amount without sales tax amount without sales tax.6 x.6 x.6x.6 x.6x.6 x So, the discounted price without sales tax is $. The sale price is % % 7% of the original price. Answer the question: is 7% of what number? a p w.7 w w So, the original price of the helmet is $. 97

34 Fair Game Review So, (.5) So, 5(.)( ) So, (.5)( ) C; meter. feet, so the measurement. feet is greater than meter. Section Activity (pp. 5 5). a. I Prt 6 (.6) At the end of 6 months, you earn $ in interest. So, your balance is $..6.5 b. I Prt ( ) At the end of month, you earn $.5 in interest. So, your balance is $ + $.5 $.5. I Prt (.6) At the end of months, you earn $ in interest. So, your balance is $ + $ $. I Prt (.6).5 At the end of months, you earn $.5 in interest. So, your balance is $ + $.5 $.5. I Prt (.6) At the end of months, you earn $ in interest. So, your balance is $ + $ $. 5 I Prt (.6).5 At the end of 5 months, you earn $.5 in interest. So, your balance is $ + $.5 $.5. Time Interest Balance month $ $ month $.5 $.5 months $ $ months $.5 $.5 months $ $ 5 months $.5 $.5 6 months $ $ Account Balance Balance (dollars) Months 9

35 . Sample answer: A credit card allows you to purchase items and then pay later. But, each month the credit card company charges interest on the unpaid balance. For example, a typical family owes $5 on their credit card and the interest rate is % per year. After one month, the interest owed is 5(. ) $75. So, the balance is $575.. a. $6 trillion $6,,,, So, this number has zeros. b. I Prt 6,,,,(.)( ) 6,,, So, the United States pays $6,,,, or $6 billion, in interest each year on its national debt. c. I Prt 6,,,,(.) 65,56,6. So, the United States pays $,56,6. in interest each day on its national debt. d. interest paid per person interest paid population 6,,,,, So, each person pays about $59.55 per year toward the national debt.. Sample answer: To find the amount of simple interest earned on a savings account, use the formula I Prt, where I is the simple interest, P is the principal, r is the annual interest rate (in decimal form), and t is the time (in years). I Prt (.)( ) 6 The amount of interest earned on a savings account with rincipal of $ at an annual interest rate of % after years is $6. To find the amount of interest owed on a loan, use the formula I Prt. I Prt (.5)( 5) 5 The amount of interest owed on a loan of $ with an annual interest rate of 5% after 5 years is $ On Your Own (pp. 5 55) I Prt ( ) So, the balance is $5 + $.5 $5.5 after 9 months... I Prt ( r)( ) r. r So, the annual interest rate of the account is., or %. I Prt 75,. 75 t.5 t ( )( t) So, the account earns $75 in interest in.5 years.. I Prt ( )( ) 6.5 So, you pay $6 + $ $7 after two years. If you pay off the loan in years instead of 5 years, you will save $5 $7 $ Exercises (pp ) Vocabulary and Concept Check. In the formula I Prt, I is the simple interest, P is the principal, r is the annual interest rate (in decimal form), and t is the time (in years).. a. When you borrow money, you want a lower interest rate because the lower the interest rate, the less you will pay for the loan. b. When you open a savings account, you want a higher interest rate because the higher the interest rate, the more money you will earn.. Before using the formula I Prt, you need to convert the percent to decimal form and you must convert the number of months to a fraction of a year. Practice and Problem Solving. a. I Prt ( )( ) So, the interest earned is $6 after years. b. The balance is $6 + $6 $66 after years. 5. a. I Prt ( )( ) 5. 5 So, the interest earned is $ after 5 years. b. The balance is $5 + $ $ after 5 years. 6. a. I Prt ( )( ) 5. 5 So, the interest earned is $5 after years. b. The balance is $5 + $5 $55 after years. 99

36 7. a. ( ) I Prt So, the interest earned is $9.5 after months. b. The balance is $ + $9.5 $9.5 after months.. a. I Prt ( )( ) I Prt 6.67 () r 6.67.r.5 r So, the annual interest rate is about.5, or.5%. So, the interest earned is $6 after 6 years. b. The balance is $7 + $6 $6 after 6 years. 9. a. I Prt ( )( ) So, the interest earned is $. after years. b. The balance is $675 + $. $9. after years.. a. I Prt ( )( ) So, the interest earned is $. after. years. b. The balance is $95 + $. $969. after. years.. a. ( ) 5 I Prt So, the interest earned is $7. after 5 months. b. The balance is $5 + $7. $69. after 5 months.. To use the formula I Prt, you must convert the number of months to years: months.5 years ( )( ) I Prt So, the interest earned is $5 after months. I Prt r. r ()() r So, the annual interest rate is., or %. I Prt r.75 r ( r)( ) So, the annual interest rate is.75, or 7.5%. I Prt 5 9( ) r 5 5r. r So, the annual interest rate is., or % I Prt 5. 5t t ( )( t) So, the amount of time is years. I Prt t t ( )( t) So, the amount of time is years. I Prt ( )( t) t.5 t So, the amount of time is.5 years. I Prt t.5 t ( )( t) So, the amount of time is.5 years.. I Prt ( )( )...5 So, the balance is $ + $ $ after years. I Prt 9 () r r.6 r So, the annual interest rate is.6, or 6%. I Prt t t ( )( t) So, it will take years to earn $6 in interest.. I Prt ( )( ) So, you pay $5 + $7 $77 for the loan.

37 5. I Prt ( )( ). 7 So, you pay $ + $7 $7 for the loan. 6. I Prt ( )( ) So, you pay $ + $6 $66 for the loan. 7. I Prt ( )( ) So, you pay $ + $9. $67. for the loan.. I Prt ( )( ) 9..., I Prt.75 P P 5 P I Prt ( ) ( )( t) 55 5, t t I Prt 5.5,( ) 5 r 5.5,r.55 r Table for Principal Interest Rate Time. principal $75.5 I Prt 75.5(.) 5.7 So, the total amount paid for the trip is about $ $5.7 $... interest $65 $5 $5 I Prt 5 5(.75)( t) 5 75t t Simple Interest $,.5% 5 years $55. $5 6.5% months $.75 $5,5.75% years $55. $, 5.5% 5 months $5.5 So, it will take years for the balance of the account to be $65.. I Prt ( )( ) 5. 5 The total that will be paid for the loan is $5 + $5 $5. So, the loan is for years, or months. So, the monthly payment is $5 $ For $ to double, that means $ is earned in interest to obtain a balance of $. Use the simple interest formula for I, P, and r.. Then solve for t. I Prt (.)( t) 6t.5 t So, it will take.5 years for $ to double at a simple interest rate of %. 6. Find the simple interest on the first loan. I Prt (.75)( ) The simple interest for the first loan is $. So, the simple interest for the second loan is $ $ $. Find the principal for the second loan. I Prt P(.)( ).6P P So, the principal for the second loan is $. 7. Interest after year: I Prt ( )( ) 5. Balance after year: $5 + $ $5 Interest after years: I Prt 5(.)( ). Balance after years: $5 + $. $5. Interest after years: I Prt 5.(.)( ).6 Balance after years: $5. + $.6 $56. Fair Game Review. x + 5 < 5 5 x < 9. b + + b. w w

38 . A; x + 5 x x 6 x 6 x The solution is x. Quiz The number of inches increases. So, the percent of change is ercent of increase. new amount percent of increase 6, or % So, the number of inches increased %.. The number of miles decreases. So, the percent of change is ercent of decrease. new amount percent of decrease 9., or % So, the number of miles decreased %.. The discount is % of $. a p w. sale price original discount 7 So, the sale price is $7.. percent of discount original price sale price original price , or 5% So, the percent of discount is 5%. 5. The sale price is % 75% 5% of the original price. Answer the question: 7.75 is 5% of what number? a p w w 99 w So, the original price is $ The markup is 5% of $5. a p w selling price cost to store + markup So, the selling price is $. 7. I Prt ( )( ) So, the simple interest earned is $. I Prt t t ( )( t) So, the time is year. I Prt r.75 r ( r)( ) So, the annual interest rate is.75, or.75%. I Prt 9. P.6 9..P P ( )( ) So, the principal is $.. The amount of error is 5 5. percent error 5 7.7, or about 7.% The percent error is about 7.%.. The first discount is % of $. a p w. 69 sale price original discount 69 6 The second discount is 5% of $6. a p w So, the final price is $6 $.5 $6.5.

39 . percent of discount original price sale price original price 5 5.5, or 5% So, the percent of discount is 5%.. Option : Because of the $75 cash back, the principal is $ $75 $5. I Prt 5(.5)( ) 7.75 If you pay off the loan in years, you will pay $5 + $7.75 $.75 for the loan. Option : Option is no interest for years so, if you pay off the loan in years, you will pay $ for the loan. Because $ < $.75, Option saves more money. 5. I Prt ( )( ). So, you pay $ + $ $ for the loan. Chapter 6 Review. 76% 76.%.76 Check:. 6% 6.%.6 Check: 5... % Check: % Check: % 5 5% is less than 5%. So, 5% is the greater number.. % 5 5 % is less than 5%. So, 5% is the greater number % 6% is greater than %. So,.6 is the greater number.....%.% is less than %. So, % is the greater number.. % % % % 5. % % % % % % The numbers in order from least to greatest are %,. %.%. Check:, and % % % 9.5 5% 5% % Check: % 5% % 5% % The numbers in order from least to greatest are.5, %, and 9.

40 . 66% 66.% The numbers in order from least to greatest are 66%,, and % % 9.% The numbers in order from least to greatest are 7,., and 9%. p 6 p p p So, % of 6 is. p 5 p 5 p 5 p So, is 5% of. 9% a 7 7 a 7 7 a a 9 So, 9 is 7% of w w w w w w So, is 75% of. 9. a p w. 5 6 So, 6 is % of 5... a p w 9 p 9 p.5 p Because.5 equals 5%, 9 is 5% of. a p w 6. p 6. p.9 p Because.9 equals 9%, 6. is 9% of.. a p w 9. w 9.w.. 7 w So, 9 is % of 7.

41 . a p w..5 w..5w.5.5 w So,. is 5% of.. a p w. 6.6 So, 6.6 is % of. 5. Answer the question: is 5% of what number? a p w.5 w.5w.5.5 w There are parking spaces. 6. a p w 6 p p p Because.6 equals 6%, 6% of the students brought cameras. 7. The number of yards increases, so the percent of change is ercent of increase. new amount percent of increase , or 5% So, the number of yards increased 5%.. The number of meals decreases, so the percent of change is ercent of decrease. new amount percent of decrease , or about 56.7% So, the number of meals decreased about 56.7%. 9. The amount of error is 6 6. percent error 6 5., or about.% The percent error is about.%.. The discount is 5% of $5. a p w sale price original price discount So, the sale price is $.5.. The sale price is % % %. Answer the question: 75 is % of what number? a p w 75. w 9.75 w So, the original price is $ So, the interest earned is $6 after years.. a. I Prt ( )( ) b. The balance is $ + $6 $6 after years..5 So, the interest earned is $ after years.. a. I Prt ( )( ). 6. b. The balance is $ + $ $ after years. I Prt r.7 r ()() r 5. I Prt r.7 r ()() r So, the annual So, the annual interest interest rate is.7, rate is.7, or 7.%. or.7%. I Prt t t ( )( t) So, the amount of time is years. 7. I Prt t 6 t ( )( t) So, the amount of time is 6 years. 5

42 . I Prt 6 ( r) 5r. r So, the annual interest rate is., or %. Chapter 6 Test..96%.96% % 65.% % 5.7% % % % % 5 5 6% is less than 65%. So, 65% is the greater number.. 56% 56.% is less than 5.6. So, 5.6 is the greater number. 9. 5% 5.% % The numbers in order from least to greatest are 5,., and 5%.. 5.% 5.% % The numbers in order from least to greatest are.5, 5.%, and 7. p p p 75 p So, 75% of is. 6 p p 5 p 5 6 p So, 6 is 6% of. a p w a a. 5 6 So, 6 is % of 5. 6

43 . a p w 6. w 6. w.. 75 w So,.% of 75 is The number of strikeouts increases, so the percent of change is ercent of increase. new amount percent of increase 6.5, or 5% So, the number of strikeouts increased 5%. 6. The amount of money decreases, so the percent of change is ercent of decrease. new amount percent of decrease 6.5, or 5% So, the amount of money decreased 5%. 7. The discount is 5% of $5. a p w sale price original price discount So, the sale price is $.5.. The markup is 75% of $5.5. a p w selling price cost to store + markup So, the selling price is $9.6.. You: % 5 Cousin:.. % Friend: 7.5% Cousin You Friend 7.5% % 5% 9% 7.5% is the greatest number. So, your friend made the most free throws.. a. The amount of error is amount of error percent error actual amount , or % The percent error is %. b. To get the same percent error, the amount of error needs to be the same. Because your estimate was 9 cars below the actual number, an estimate of 9 cars above the actual number will give the same percent error. So, the other estimate that gives the same percent error is cars... Interest after year: I Prt ( )( ) Balance after year: $ + $ $ Interest after years: I Prt (.)( ) 6 Balance after years: $ + $6 $6 Interest after years: I Prt (.)( ) 96 Balance after years: $ + $96 $96 Chapter 6 Standards Assessment. C; a p w..5 $.55 discounted price regular price discount $.5 $.55 $ I Prt ( )( ) So, the interest earned is $6 after years.. I Prt ( )( ) 7 P.5 7.P 9 P So, the principal is $9. 7