Math Fundamentals for Statistics (Math 52) Homework Unit 6: Rates/Ratios/Proportions Scott Fallstrom and Brent Pickett The How and Whys Guys Homework Unit 6 Page 1
6.1: Comparing Objects Ratios and Rates Vocabulary and symbols write out what the following mean: Ratio Rate Per Unit rate Concept questions: 1. What is the difference between a ratio and a rate? 2. If you were travelling at 80 miles per hour, how far would you travel in an hour? 3. If you were travelling at 80 miles per hour, how far would you travel in half an hour? 4. If you were travelling at 80 miles per hour, how far would you travel in 15 minutes? 5. If a number is divided by 43, could we ever have a remainder of 50? Why or why not? 6. If you buy one Krispy Kreme doughnut, it costs $1.40. If you buy a dozen, the cost is $11.51 and two dozen is $19.99. Find the unit price of a doughnut with each option. Which option would you choose? Exercises: 7. Find different way to represent $45 per hour as a rate. a. dollars per minute b. dollars per day (8-hour day) c. dollars per week (40 hour wk) d. cents per minute e. 7 hours for f. 20 minutes for 8. Find different way to represent 60 miles per hour as a rate. a. miles per minute d. minutes per mile b. miles per second e. 7 hours covers c. seconds per mile f. 20 minutes covers 9. Find different way to represent 36 miles per gallon as a rate. a. gallons per mile d. miles per quart b. gallons per hundred miles e. miles per ounce c. miles per half-gallon f. 180 miles uses 10. If a jug of laundry detergent has 150 ounces for $20.19, and says it contains enough for 110 loads. a. cents per load d. cents per ounce b. ounces per load e. loads per dollar c. ounces per cent f. 40 loads for $ Homework Unit 6 Page 2
11. Write the following as unit rates. It may be helpful to know that 1 pound = 16 ounces. a. b. c. d. e. f. g. h. Quantity Unit Rate Desired Rate (Fraction) $9 for 3 pounds dollars per pound $9 for 3 pounds cents per pound $9 for 3 pounds dollars per ounce $9 for 3 pounds cents per ounce $9 for 3 pounds pounds per dollar $1.99 for 150 tissues dollars per napkin $1.99 for 150 tissues napkins per dollar $1.99 for 150 tissues napkins per penny i. j. 720 miles on 19.8 gallons of gas 720 miles on 19.8 gallons of gas miles per gallon gallons per mile Wrap-up and look back: 12. If you see a cost of 20 cents per load on one detergent and $23.99 for 115 loads, which is a better buy? Explain your reasoning using unit rates. 13. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. Homework Unit 6 Page 3
6.2: Proportions Vocabulary and symbols write out what the following mean: Proportionate Proportion Variable Concept questions: 1. If you have a ratio of 5:1 and you add more in a ratio of 3:1, would the new ratio be 5:1? Explain your answer. 2. If you have a ratio of 5:1 and you add more in a ratio of 3:1, what can you say about the new ratio? 3. If you have a ratio of 5:1 and you add more in a ratio of 7:1, would the new ratio be 5:1? Explain your answer. 4. If you have a ratio of 5:1 and you add more in a ratio of 7:1, what can you say about the new ratio? 5. If you have a ratio of 5:1 and you add more in a ratio of 5:1, would the new ratio be 5:1? Explain your answer. 6. If you were putting in 20 grams of flour and 30 grams of sugar, could you add 10 grams of each and keep the same ratio? 7. If you were putting in 20 grams of flour and 30 grams of sugar, could you multiply both amounts by 5 for each and keep the same ratio? 8. What operations can we use to keep the same ratio: addition/subtraction/multiplication/division? Explain with examples. 9. If you had a proportion and just flipped over the fraction on each side, is it still a proportion? Explain. Exercises: 10. Using the rule from the textbook, determine if the following are true proportions. a. b. c. d. e. 11 55 24 120 3 2.1 4 2.8 9 21 11 23 22 51.7 26 61.1 21 34 34 55 f. g. h. i. 21 7 5 1 1 3 7 9 10 8 9 15 22 8 13 13 21 8 13 Homework Unit 6 Page 4
11. Write the proportion in at least 3 different ways (correctly). a. b. 3 5 6 10 1 11 7 77 c. d. 3 x 5 9 2 x 7 19 e. f. A C B D 13 5 M 11 12. Rewrite the proportion as an equation without any fractions. 3 x 3 x a. c. 5 10 5 9 b. 1 11 x 77 d. 2 x 7 19 e. f. A C B D 13 5 M 11 13. Solve the proportions. a. 3 x 5 10 d. 2 x 7 19 g. 13 5 M 11 b. c. 1 11 x 77 3 x 5 9 e. f. 9 x 11 13 21 x 23 1173 h. x 7 11 22 7 3 2 14. For these problems, set up a proportion, and then solve the proportion. Write the final result as a sentence. a. A doctor prescribes 30 ounces of medicine for every 25 pounds of body weight. How much medicine would we give to a child weighing 105 pounds? (round to 1 decimal place) b. A doctor prescribes 250 mg of medicine for every 60 pounds of body weight. How much medicine would we give to a child weighing 105 pounds? (round to 1 decimal place) c. A doctor prescribes 250 mg of medicine for every 60 pounds of body weight. How much medicine would we give to a child weighing 105 pounds? (round to 1 decimal place) d. If you paid $9.49 in tax on a $115 purchase, how much tax would you pay on a purchase of $379.85? e. A recipe calls for 3 cups of flour and 1 cup of sugar. Jasmine has only 2 cups of flour left how much sugar should she put in to keep the recipe proportionate? Homework Unit 6 Page 5
f. A recipe for chocolate chip cookies says that one package of chocolate chips (12 ounces) needs to 1 be combined with 2 cups of flour. Costco sold a bag that had 5 pounds of chocolate chips how 4 much flour would need to be added? (1 pound = 16 ounces) g. A McCulloch chainsaw requires a gas-oil mix, in a ratio of 50:1. How many fluid ounces of oil do you need to add to one gallon of gasoline? [Note: One gallon contains 128 fluid ounces.] h. Scott s Grass seed (Turf Builder) is sold in 7 pound bag for $34.19. The bag says it will cover up to 2,800 sq. ft. How many bags should I buy and how much will it cost for me to get enough fertilizer to cover my lawn if the lawn is a rectangle that is 120 feet by 80 feet? Wrap-up and look back: 15. Where else have you seen ratios and proportions in your life? 16. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. 6.3: Percents Vocabulary and symbols write out what the following mean: Percent Proportion Variable Concept questions: 1. Where did percent come from as a word? 2. Can we write any ratio as a percent? Explain. 3. Does writing 7 for every 20 as a percent change the value? Explain. 4. If you got a 75% on your quiz, and Simone got 11 out of 15, who had the better score? 5. If you pay $9.49 in tax on a purchase of $115, what is the tax percent rate? Exercises: 6. Write the following ratios as percents. a. 7 for every 23 b. 9 for every 11 c. 47 for every 13 d. 97 out of 150 e. 67 out of 200 f. 7 out of 8 g. 43 out of 21 h. 16 for 50 i. 211 for 795 j. 4,256 out of 14,053 (Pete Rose) Homework Unit 6 Page 6
7. Convert these fractions or decimals into percents. a. 7 20 b. 11 23 c. 23 57 d. 79 83 e. 6,451 93,778 12,192 f. 24,537 g. 0.052 h. 0.956 i. 1.54 j. 2.85 k. 16.394 l. 0.0025 (Michael Jordan) 8. Convert these percents into decimals. a. 45.7% 3 e. 5 % b. 91% 8 c. 0.278% f. 6.315% d. 195% 44 g. 99 % (Ivory Soap) 100 9. Complete the table to show the different ways to write the expression. a. b. c. d. Ratio 9:23 Fraction or Mixed Number 15 9 Decimal 6.67 Percent 4.23% 10. EXPLORE! Complete the table to show the different ways to write the expression. a. b. c. d. Ratio Fraction Decimal Percent 27:12 1 694 3 0.023 0.25% Homework Unit 6 Page 7
11. What percent interest would be earned if you earned $9.25 on an investment of $78.95 over one year? (this would be as a percent per year) 12. If you took out a loan and were charged $50 in interest on a loan of $600, what is the percent? What is the percent per year? 13. If you took a loan from Money-Tree, you are charged a fee. In California, the fee is about $8.83 for a $50 loan over 14 days. a. What percent is this fee? (be sure to include the length of time) b. How many weeks is 14 days? c. How many weeks are in a year? d. Determine the rate as a percent (per year) by setting up and solving a proportion. e. Would you recommend this loan? 14. Mortgages are often reported as percentages in mixed-number form. Determine the decimal 1 percentage rates for the following mortgages. EX: 5 % 5.1% 10 3 7 5 a. 5 % c. 3 % e. 4 % 8 8 8 1 1 1 b. 2 % d. 4 % f. 4 % 4 4 2 Wrap-up and look back: 15. Where else have you seen percentages in real life? 16. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. 6.4: Solving Percent Problems Vocabulary and symbols write out what the following mean: Percent Increase Percent Decrease Concept questions: 1. If you had a percent increase, would this result in multiplying by a decimal number bigger or smaller than 1? Explain. 2. If you had a percent decrease, would this result in multiplying by a decimal number bigger or smaller than 1? Explain. 3. Can we have a percent increase of 100% or more? Explain with an example. Homework Unit 6 Page 8
4. Can we have a percent decrease of 100%? Explain with an example. 5. Can we have a percent decrease of more than 100%? Explain with an example. 1 6. If we have a percent decrease of 50%, would that be the same as just multiplying by? Example. 2 7. A sign indicates that if you use this coupon, you ll save 120%. What is wrong with the sign? 8. If you used a coupon for 20% off and another coupon for 40% off, would you expect to save more or less than 60%? Explain. 9. Does the order of coupons matter: if you used a 20% off coupon and then a 30% off coupon, would you get a better deal than using the 30% coupon and then the 20% off coupon? Explain. 10. If going from A to B results in a 10% decrease, does going from B to A result in a 10% increase? 11. If going from A to B results in a 10% increase, does going from B to A result in a 10% decrease? 12. If we know the percent increase, can we use it to quickly find the percent decrease? 13. Is a 5% increase on the starting amount the same as 105% of the starting amount? Exercises: 14. Solve these percent problems using a percentage bar. a. What is 40% of 300? b. What is 30% of 250? c. 50 is what percent of 30? d. 40 is what percent of 82? e. 20 is 14% of what? f. 18 is 80% of what? 0% 100% 15. Find the missing value in these percent problems using proportions/equations. a. What is 35% of 45? e. What percent is 30 of 55? b. 125% of 60 is what? f. 20 is 67% of what? c. What percent of 80 is 75? g. 150% of what is 84? d. What percent of 900 is 75? h. 52 out of 90 is what percent? 16. If you paid $8,524 in property tax on a home valued at $554,000, what percent tax did you pay? 17. If you paid $82.08 for an item (with tax included), and the price on the shelf was $75, what percent of the $75 did you pay? What was the sales tax rate as a percent? 18. John ate 3 of the 8 equal slices of pizza. What percent of the whole pizza did he eat? 19. Martha saw that each cupcake was cut into 4 pieces. She ate 11 pieces. What percent of one cupcake did she eat? Homework Unit 6 Page 9
20. If possible, find the relationship to the original amount as a decimal and percent if you know the following: a. 10% decrease b. 40% increase c. 35% decrease d. 11% increase e. 50% decrease f. 50% increase g. 12% increase h. 12% decrease i. 149% increase j. 149% decrease k. 100% decrease l. 12,415% increase 21. Determine the percent increase or decrease using either method from the textbook. a. b. c. d. e. f. g. h. Start End Increase or Decrease Percent 100 40 100 140 20 40 40 20 50 75 75 50 20 60 60 20 22. Use the percent increase or decrease to find the final amount. a. Property taxes were $11,026 this year but increased by 4.2%. How much would we pay next year? b. An item at Disneyland was priced at $32.38. Once you include the 8.1% sales tax, how much would you pay total? c. If you wanted a price to be $50 (with tax included), how much would you put as the price on the shelf if the sales tax was 8.25%? d. If Josue was making $28.15 per hour and earned an 11% increase, how much would he earn per hour after the raise? e. Faculty members at Palomar were paid $70,000 per year to start. However, during negotiations, the starting salary was cut by 1.8%; what is the new starting salary? f. Someone making $42,000 per year and getting a 2.3% raise would make how much the next year? Homework Unit 6 Page 10
g. An item is $59.99 on the shelf and you have a coupon for 40% off. The sales tax where you are is 4.58%. i. How much is the sale price (price after the coupon)? ii. How much is your total price (sale price plus tax)? h. While at a Kohl s sale, a customer brought in two coupons one for 10% off, and one for 30% off to be used one after another on an item that costs $74.95. i. Determine the final price if you used the 10% off coupon first, then the 30% off coupon. ii. Determine the final price if you used the 30% off coupon first, then the 10% off coupon. iii. What property we learned guarantees this will always happen? Wrap-up and look back: 23. Which method of solving percent problems is your favorite: the bar or the proportion/equation? Explain your answer. 24. If the percent increase is 20%, set up a proportion that will allow you to find the percent decrease required to bring the item back down to the original price. [NOTE: This is a reasonably common practice that retailers use to have a sale that brings in more people, but the sale brings the price back down to the same price it was before the sale. Buyer beware!] 25. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. 6.5: Percent Problems with Money Vocabulary and symbols write out what the following mean: Simple Interest Average Daily Balance I P r t Concept questions: 1. When you are told an interest rate as a percent, do you need to know the time as well? Explain. 2. Which one is better to invest with: 5% annual interest or 6% annual interest? Explain. 3. Which one is better to borrow with: 5% annual interest or 6% annual interest? Explain. 4. Which one is better to borrow with: 10% annual interest or 1% monthly interest? Explain. 5. Which one is better to invest with: 10% annual interest or 1% monthly interest? Explain. 6. Which one is better to invest with: 60% annual interest or 5% monthly interest? Explain. Homework Unit 6 Page 11
Exercises: 7. Find the amount of simple interest earned on an investment of $890 at 6% annual interest for 3 years. 8. Find the amount of simple interest earned on a. an investment of $890 at 8% annual simple interest for 15 months. b. an investment of $12,590 at 7.25% annual simple interest for 8 years. c. an investment of $1,150 at 8.9% annual simple interest for 3 days. d. an investment of $90 at 4.2% annual simple interest for 13 weeks. 9. Find the amount of simple interest earned on a. an investment of $890 at 8% monthly simple interest for 15 months. b. an investment of $12,590 at 1.25% monthly simple interest for 3 years. c. an investment of $1,150 at 0.08% daily simple interest for 7 days. d. an investment of $90 at 0.2% daily simple interest for 13 weeks. 10. Find the amount of simple interest owed on a. a loan of $1,500 at 5.25% annual simple interest for 6 months. b. a loan of $5,500 at 4.25% annual simple interest for 6 years. c. a loan of $500 at 17.99% annual simple interest for 2 years. 1 d. a loan of $17,500 at 4 % annual simple interest for 6 years. 2 1 e. a loan of $17,500 at 4 % monthly simple interest for 6 years. 2 3 f. a loan of $4,000 at 11 % annual simple interest for 5 years. 4 Wrap-up and look back: 11. Is there a reason why a 5% interest rate would be better than 20% interest when you are taking out a loan? Explain your answer. 12. In the formula I P r t, if Isaac puts in 20 for r because it is 20% annual simple interest, will his answer be correct? Explain what he should do if he was incorrect. 13. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. Homework Unit 6 Page 12
6.6: Slope Vocabulary and symbols write out what the following mean: Slope Concept questions: 1. When finding the slope, is it change in y over change in x, or vice versa? 2. If a line goes up from left to right, the slope is positive, negative, or zero? 3. If a line goes down from left to right, the slope is positive, negative, or zero? 4. If a line stays flat from left to right, the slope is positive, negative, or zero? Exercises: 5. If possible, find the slope of the line from the two points given; simplify any fractions. a. 8,11 and 16,19 e. 1, 7 and 8, 3 b. 2, 5 and 31, 5 c. 1,14 and 1,10 d. 5, 4 and 1, 4 f. 11, 4 and 20, 10 g. 1, 4 and 20, 10 h. 11, 4 and 20,10 6. Determine the units of measure on the slope if a. y-coordinate measures gallons and x-coordinate measures hours. b. y-coordinate measures meters and x-coordinate measures hours. c. y-coordinate measures crayons and x-coordinate measures minutes. d. y-coordinate measures beats and x-coordinate measures seconds. e. y-coordinate measures hours and x-coordinate measures miles. f. y-coordinate measures years and x-coordinate measures bananas. g. y-coordinate measures dollars and x-coordinate measures pounds. h. y-coordinate measures pounds and x-coordinate measures dollars. 7. Answer the following questions about the graph (next page). a. What two points are on the graph? (0, ) and (6, ) b. Find the slope of the line from the points on the graph. c. Interpret this slope using a sentence and the appropriate units. d. Interpret the two points using sentences. e. Using the graph, about how much would 4 pounds of cheese cost? Homework Unit 6 Page 13
8. Answer the following questions about the graph (below). a. What two points are on the graph? (0, ) and (18, ) b. Find the slope of the line from the points on the graph. c. Interpret this slope using a sentence and the appropriate units. d. Interpret the two points using sentences. e. Using the graph, what would the temperature be at 7:06 pm? f. Using the graph, what would the temperature be at 7:14 pm? 9. At a concert, there were 46,000 people at 8pm and 54,000 people at 10pm. Find and interpret the slope of the line between these points if people are on the y-axis. Homework Unit 6 Page 14
10. An electrician charges $400 for a 4 hour job, and $520 for a 6 hour job. Find and interpret the slope of the line between these points if the dollars are on the y-axis. 11. Use the graph to find and interpret the slope of the line between the points. a. b. c. Homework Unit 6 Page 15
Wrap-up and look back: 12. If you were given two points, can you find the slope? Did you need a formula? 13. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. 6.7: Geometry and Ratios Vocabulary and symbols write out what the following mean: Slope Concept questions: 1. If you double the radius, what happens to the circumference of the circle? What about the area? What about a sphere? 2. If you triple the radius, what happens to the circumference of the circle? What about the area? What about a sphere? 3. In a rectangle, if you double the length and triple the height, what is the ratio of the new rectangle s area to the original? Exercises: 4. Use the table below to find the circumference quickly. Circumference of a circle based on radius 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.00 0.63 1.26 1.88 2.51 3.14 3.77 4.40 5.03 5.65 1 6.28 6.91 7.54 8.17 8.80 9.42 10.05 10.68 11.31 11.94 2 12.57 13.19 13.82 14.45 15.08 15.71 16.34 16.96 17.59 18.22 3 18.85 19.48 20.11 20.73 21.36 21.99 22.62 23.25 23.88 24.50 4 25.13 25.76 26.39 27.02 27.65 28.27 28.90 29.53 30.16 30.79 5 31.42 32.04 32.67 33.30 33.93 34.56 35.19 35.81 36.44 37.07 6 37.70 38.33 38.96 39.58 40.21 40.84 41.47 42.10 42.73 43.35 7 43.98 44.61 45.24 45.87 46.50 47.12 47.75 48.38 49.01 49.64 8 50.27 50.89 51.52 52.15 52.78 53.41 54.04 54.66 55.29 55.92 9 56.55 57.18 57.81 58.43 59.06 59.69 60.32 60.95 61.58 62.20 a. A circle with radius 3.2 yards. b. A circle with radius 5.5 miles. c. A circle with radius 6.4 feet. d. A circle with diameter 2.8 feet. e. A circle with diameter 7.8 cm. f. A circle with diameter 18.6 yards. Homework Unit 6 Page 16
5. Use the table below to find the circumference quickly. Area of a circle based on radius 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.00 0.03 0.13 0.28 0.50 0.79 1.13 1.54 2.01 2.54 1 3.14 3.80 4.52 5.31 6.16 7.07 8.04 9.08 10.18 11.34 2 12.57 13.85 15.21 16.62 18.10 19.63 21.24 22.90 24.63 26.42 3 28.27 30.19 32.17 34.21 36.32 38.48 40.72 43.01 45.36 47.78 4 50.27 52.81 55.42 58.09 60.82 63.62 66.48 69.40 72.38 75.43 5 78.54 81.71 84.95 88.25 91.61 95.03 98.52 102.07 105.68 109.36 6 113.10 116.90 120.76 124.69 128.68 132.73 136.85 141.03 145.27 149.57 7 153.94 158.37 162.86 167.42 172.03 176.71 181.46 186.27 191.13 196.07 8 201.06 206.12 211.24 216.42 221.67 226.98 232.35 237.79 243.28 248.85 9 254.47 260.16 265.90 271.72 277.59 283.53 289.53 295.59 301.72 307.91 a. A circle with radius 3.2 yards. b. A circle with radius 5.5 miles. c. A circle with radius 6.4 feet. d. A circle with diameter 2.8 feet. e. A circle with diameter 7.8 cm. f. A circle with diameter 18.6 yards. 6. Use a rectangle with base of 10 inches and height of 14 inches. a. Then double both height and base. Find the ratio of the areas (compare the new to the old). b. Then triple both height and base. Find the ratio of the areas (compare the new to the old). 7. Use a square with sides of 31 feet. Then double the side lengths. Find the ratio of the areas (compare the new to the old). 8. Use a triangle with base of 10 inches and height of 14 inches. a. Then double both height and base. Find the ratio of the areas (compare the new to the old). b. Then triple both height and base. Find the ratio of the areas (compare the new to the old). 9. Compute the ratio of the new shape to the original with the given details for these examples, use the formulas instead of tables and don t round! a. Original shape: circle with radius of 8.1 inches; New shape: circle with radius of 16.2 inches. Compare the circumferences. b. What happens to the circumference of a circle when you double the radius? c. Original shape: circle with radius of 8.1 inches; New shape: circle with radius of 16.2 inches. Compare the areas. d. What happens to the area of a circle when you double the radius? e. What happens to the area of a triangle when you double the base and height? f. What happens to the area of a triangle when you triple the base and height? Homework Unit 6 Page 17
10. 3-dimensional extensions. Compute the ratio of the new shape to the original with the given details for these examples, use the formulas instead of tables and don t round! a. Original shape: sphere with radius of 4 inches; New shape: sphere with radius of 8 inches. 2 Compare the surface areas. SA 4 r b. What happens to the surface area of a sphere when you multiply the radius by 2? c. Original shape: sphere with radius of 4 inches; New shape: sphere with radius of 8 inches. 4 3 Compare the volumes. V r. 3 d. What happens to the volume of a sphere when you multiply the radius by 2? e. What happens to the surface area of a sphere when you multiply the radius by 4? SA 4 r Wrap-up and look back: 11. How does the number you multiply dimensions by affect the a. Perimeter? b. Area? c. Volume? 12. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. 6.8: Dimensional Analysis and Unit Conversions Vocabulary and symbols write out what the following mean: Dimensional Analysis Unit Conversions Concept questions: 1. When doing dimensional analysis, why are we able to cross out a unit on top and the same unit on bottom? Does this relate back to fractions? 2. Why do we call them unit conversions? (there may be more than one correct response!) 3. Explain what happens when we create a ratio with any two items that are equal. 4. If we convert F feet into inches, would the result be larger or smaller than F? Why? 5. If we convert F feet into yards, would the result be larger or smaller than F? Why? 6. If we convert P pounds into ounces, would the result be larger or smaller than P? Why? 7. If we convert P pounds into tons, would the result be larger or smaller than P? Why? 8. If we convert G grams into milligrams, would the result be larger or smaller than G? Why? 2 Homework Unit 6 Page 18
Exercises: Distance Area Volume Weight/Mass 1 foot = 12 inches 1 ft 2 =144 in 2 1 gallon = 231 in 3 1 lb = 16 oz 1 yard = 3 feet 1 yd 2 = 9 ft 2 1 gallon = 128 fl. oz. 1 ton = 2,000 lb 1 mile = 5,280 feet 1 acre = 43,560 ft 2 1 L = 1000 ml 1 kg 2.204 lb 1 inch = 2.54 cm 1 cm 2 = 100 mm 2 1 gal = 4 qt 1 g = 1,000 mg 1km = 1,000 m 1 m 2 = 10,000 cm 2 1 qt = 2 pt 1 kg = 1,000 g 9. Convert the units as shown in the text. a. How many feet are in 15 miles? b. How many inches in 18 centimeters? e. How many miles are in 10,000 inches? f. How many square inches are in 10 square feet? g. How many square feet are in 10 square yards? h. How many square feet are in 10 square miles? i. How many square centimeters are in 10 square feet? j. How many square yards are in 80,000 square cm? k. How many cubic feet are in 6 cubic yards? l. How many seconds are in 14 days? m. How many minutes are in one year? n. If you waited for 100,000 minutes, how many days is this? c. How many yards are in 522 feet? d. How many inches are in 1.8 miles? o. One plot of land is a rectangle measuring 7,200 feet by 3,500 feet. How many acres is this? p. One plot of land is a rectangle measuring 900 yards by 742 yards. How many acres is this? q. How many km in 2 mile? r. How many miles in 5 km? s. If one US bill has a mass of 1 gram, how much would $10,000 weigh if it was $20 bills? t. If one US bill has a mass of 1 gram, how much would $10,000 weigh if it was $5 bills? u. If we were administered a drug at a rate of 22 grams per day, how much is this as mg/hour? v. Fastest woman in history, Florence Griffith-Joyner, ran 100 meters in 10.49 seconds. What would this be in miles per hour? Wrap-up and look back: 10. Converting from a larger unit to smaller unit, then the number will look ( larger / smaller )? 11. Converting from a smaller unit to larger unit, then the number will look ( larger / smaller )? 12. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. Homework Unit 6 Page 19
6.9: Applications Vocabulary and symbols write out what the following mean: None Concept questions: 1. When comparing prices, would you prefer to buy something with a higher or lower $ per pound? 2. When comparing prices, would you prefer to buy something with a higher or lower ounces per $? 3. Would you want a car with a higher or lower rate of gallons per mile? Explain why. Exercises: 4. Solve these unit rate applications: a. Costco sells Tillamook 2.5 pounds of cheese for $8.99. Albertsons has 2 pounds of the same cheese for $7.99. Which one is the better per unit price? Which one would you buy? b. Vons sells 32 ounces of sour cream for $4.29 and 24 ounces for $2.99. Which one is the better per unit price? Which one would you buy? c. Costco sells Kraft mayo at 1 gallon for $8.39. Vons sells Kraft mayo for $3.19 for 30 ounces. Which has the best unit price? Which would you buy if you needed some mayo? 5. Solve these vehicle applications: a. A new Kia Soul claims 24 mpg for city driving. How many gallons are used in 100 miles? [This is called gallons per hundred miles ] b. If gas prices are $3.699 per gallon, how much would it cost for the Soul to go 100 miles? c. A new Kia Sportage claims 21 mpg for city driving. How many gallons are used in 100 miles? d. If gas prices are $3.699 per gallon, how much would it cost for the Sportage to go 100 miles? e. Over the course of 12,000 miles (about one year of driving), which vehicle has lower gasoline costs, and how much less? 6. Geometry: There is a triangular piece of land outside a house and the family wants to turn it into a yard. The height of the triangle is 12 yards and the base is 23 feet. One bag of grass seed covers 200 square feet and costs $13.79. a. How many bags are needed? b. How much will this cost (before tax)? c. If the sales tax is 7.75%, how much will the bags cost (after tax)? Homework Unit 6 Page 20
Wrap-up and look back: 7. What type of application problems did you like best? 8. Did you have any questions remaining that weren t covered in class? Write them out and bring them back to class. 6.10: Ratios and Proportions Wrap-Up (Practice) 1. Write the following as unit rates. It may be helpful to know that 1 pound = 16 ounces. Quantity Unit Rate Desired Rate (Fraction form) $1.20 for 5 apples dollars per apple $1.20 for 5 apples apples per dollar $14.87 for 9.8 gallons dollars per gallon $14,87 for 9.8 gallons gallons per dollar $19 for 1.2 pounds ounces per cent 2. Using the rule from proportions, determine if the following are true proportions. a. 2,284 4 9.4 115 b. 2,855 5 11.2 144 3. Using the methods shown in the text, solve the following proportions. Keep the end results the same as the starting if you start with fractions/decimals, end with them. a. 11 28 11 x b. 9 x 23 1173 4. Complete the table to show the different ways to write the expression. Ratio Fraction Decimal Percent 41:20 1 5 4 0.064 65.1% Homework Unit 6 Page 21
5. Find the missing value in these percent problems. a. What percent of 2000 is 150? b. 89% of 62 is what? c. 80% of what is 32.9 d. What percent of 36 is 50? 6. Determine the percent increase or decrease using either method. Start End Increase or Decrease Percent 80 500 500 80 125 100 7. 1 Marti puts $950 in an account earning 2 % annual simple interest for 10 years. How much simple 4 interest did she earn? 8. If possible, find the slope of the line from the two points given; simplify any fractions. a. 10,11 and 14,18 b. 2,15 and 9, 5 c. 3, 3 and 8, 3 d. 14, 4 and 14, 0 e. 7, 4 and 14, 5 f. 1, 4 and 6, 6 9. Compute the ratio of the new shape to the original with the given details for these examples, use the formulas and don t round! a. Original shape: circle with radius of 15 inches; New shape: circle with radius of 45 inches. Compare the circumferences. b. What happens to the circumference of a circle when you triple the radius? 10. Convert units using the technique shown in the text. a. How many seconds are in 500 days? b. If you count a $5 bill every second, how long would it take you to count to $3,000,000? (Find this in seconds, hours, days) c. How many feet in 300 centimeters? (remember that 1 in = 2.54 cm) d. How many square yards are in 5,000 square feet? Homework Unit 6 Page 22