Proportional Reasoning and Scale: Solve Problems Using Proportions: Play Answer Sheet

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1 Name Date Proportional Reasoning and Scale: Solve Problems Using Proportions: Play Answer Sheet Selected Response Items Indicate letter or letters only Fill-in-the-Blank Items Discovery Education Techbook Discovery Communications, LLC 1

2 Proportional Reasoning and Scale: Solve Problems Using Proportions: Play Number of Questions: 15 Questions 1 9 are selected response questions. Indicate the correct response or responses for each question on your answer sheet by writing the letter(s) only. 1. Meredith is a self-employed writer. She must pay 12.4% in taxes on all her income. If she is paid $850 for a job, how much of her pay is left after she deducts the taxes? A. $ B. $ C. $ D. $ A substance decays at a constant rate of percent per unit of time. Dr. Cohn is researching the effects of a medicine to treat nausea. During an experiment, Dr. Cohn starts with 15 milligrams of the medicine and notes that 12.6 milligrams remain after 1 hour. Which equation could Dr. Cohn use to solve for p, the percent decay of the medicine in 1 hour? A. C. p 12.6 p 2.4 B p 100 p 100 D A specialty shampoo for sensitive scalps regularly costs $8.00 at the store. A store puts the shampoo on clearance for a price of $5.60 to make room for stock of the same shampoo with a new bottle design. What percent markdown did the store use to determine the clearance price? A. 24% B. 30% C. 70% D. 76% Discovery Education Techbook Discovery Communications, LLC 2

3 4. Janet constructed a model of a suspension bridge for her engineering class. The graph below represents the relationship between the length of a cable used in the model and the distance the cable is from the closest end of the bridge. Which statement demonstrates if a proportional relationship exists between y, the length of the cable, and x, the distance of the cable from the closest end of the bridge? A. No, there is not a proportional relationship, because B. No, there is not a proportional relationship, because C. Yes, there is a proportional relationship, because D. Yes, there is a proportional relationship, because Which situations can be solved using only proportional relationships? Check all that apply. A. computing the total cost for purchasing a new cell phone with prepaid phone minutes B. calculating the height of a ball thrown in the air after a given number of seconds based on the speed at which it was thrown and height from which the ball was thrown C. determining the earnings of a salesperson who earns a 40% commission from all sales D. converting a speed given in kilometers per hour to a speed in meters per second E. measuring the angle turned by the minute hand on an analog clock in a given number of minutes Discovery Education Techbook Discovery Communications, LLC 3

4 6. A contractor is designing floor plans and budget estimates for the construction of a new office for a software business. The contractor plans on charging $75 per square foot to cover labor and materials for the flooring in the lobby. The software business decides to increase the area of the lobby by 5%. Which equations represent the new estimated cost, C, of the lobby floor based on the original area, 500 square feet? Check all that apply. A. C B C C. C D. 75 C E C Tomas is preparing a grocery budget for his restaurant. He knows that he uses a 10-pound bag of onions in 3 days. A 10-pound bag of onions costs $9.50. Which statement explains if Tomas can use proportions to determine the necessary budget for onions in a month with 30 days? A. Yes. Because both days and cost are given for 10-pounds of onions, Tomas can use 3 30 the proportion for the ratios of days to cost,, to solve for x, the budget 9.5 x needed for onions in 30 days. B. Yes. Tomas can determine the number of 10 pounds bags of onions needed by multiplying by 30 days, and then using that in a proportion for the ratios of price to pounds, 9.5 x, to solve for x, the budget needed for onions in 30 days C. No. This problem requires addition to determine the price per pound of onions and the number of pounds of onions per day, and then multiplying by 30: x D. No. This problem requires subtracting the 3 days to find the cost of onions per 1 day, and then multiplying by 30 for the monthly cost: x. Discovery Education Techbook Discovery Communications, LLC 4

5 8. A store charges 2% simple interest per month for layaway of items that cost more than $100. Blake and Rita each write proportions to determine the cost of a $200 item on layaway after 1 month based on I, the interest in dollars. Blake: I 102 Rita: I 200 Which statement is true about their proportions? A. Both of their proportions are correct to solve the amount of interest for the $200 item on layaway. B. Neither of the proportions can be solved to determine the cost after interest. C. Blake s proportion is incorrect because I, the interest in dollars, is misrepresented in his proportion. Rita s proportion is correct and can be solved for I, the cost of the item plus the 2% interest. D. Blake s proportion is correct to solve for I, the 2% interest for the $200 item, but Rita s proportion is incorrect, because one of her ratios uses addition and proportions should only involve multiplication and division. 9. A school has a sump pump installed in the basement to be used in the event of flooding. The sump pump has a listed discharge rate of 2,460 gallons per hour. Which statements describe a sump pump with the same discharge rate? Check all that apply. A. A different model of sump pump lists a discharge rate of 41 gallons per minute. B. A plumber tests a sump pump that discharges 5 gallons of water in 10 seconds. C. A contractor purchases a sump pump that advertises a discharge rate of 164 quarts per minute. D. A factory has a goal to design a sump pump that discharges 6 quarts per second. E. The sump pump at a swimming pool discharges 19,680 gallons of water over 8 hours. Discovery Education Techbook Discovery Communications, LLC 5

6 Questions are fill-in-the-blank questions. Write the correct answer(s) in the spaces given on your answer sheet. 10. The proportion shown below represents the formula used by a tax calculator to determine total cost, C, of a purchase with a 7% tax based on a subtotal of x dollars. 107 c 100 x Fill in the blanks to show 2 equations for the total cost with tax, C, based on a subtotal of x dollars. C = x x C = x 11. A factory that manufactures school supplies classifies a plastic ruler as defective if there is greater than a 0.05% error in its total length of measure. Choose the equations that can be solved for x, and also the minimum or maximum allowable measure in inches of a 12-inch ruler that is not considered defective. Indicate the letter for each number in your answer sheet. A. x B Equations from Which to Choose x C x D x Minimum allowable Maximum allowable 12. Payton, Levi, and Marta want to compare interest rates for the savings accounts they hold at different banks. The table below shows the beginning and ending balances of each of their accounts after 3 months when no deposits were made: Name Beginning Balance Ending Balance Payton $ $ Levi $ $ Marta $ $ Order the friends accounts from the one that had the lowest interest rate for the 3-month period to the one that had the greatest interest rate. Indicate the letter for each number in your answer sheet. Accounts from Which to Choose A. Payton s savings account B. Levi s savings account C. Marta s savings account Lowest Interest Rate Middle Interest Rate Greatest Interest Rate Discovery Education Techbook Discovery Communications, LLC 6

7 13. Colleen is preparing a menu for a turkey dinner to feed a large group of people. She looks at a few different cookbooks and finds the following recommendations for cooking turkeys at an oven temperature of 325 F : Some of the recommendations are for stuffed turkeys, which take longer to cook than unstuffed turkeys. Classify the ordered pairs representing turkey weight in pounds, x, and cooking time in minutes, y, as proportional with the point (1, 16) for an unstuffed turkey or (1, 19) for a stuffed turkey. Indicate the letter for each number in your answer sheet. Categories from Which to Choose A. Unstuffed Turkey (1, 16) B. Stuffed Turkey (1, 19) Ordered Pair (11, 209) (12, 228) (14, 224) (16, 256) (20, 380) Category Discovery Education Techbook Discovery Communications, LLC 7

8 14. Photographs can be ordered in varying sizes. The dimensions of a rectangular photograph are shown in the diagram. Classify each size of a photograph as proportional or not proportional to a 4-inch-by-6-inch photograph. Indicate the letter for each number in your answer sheet. Classifications from Which to Choose A. Proportional B. Not Proportional Size of Photograph 8 inch by 10 inch 6 inch by 9 inch 5 inch by 7 inch 12 inch by 18 inch 10 inch by 15 inch Classification 15. Ellen gets a 25% discount on items she purchases at the store where she works. Let x represent the original price of an item in dollars. Classify each proportion or equation as determining whether y equals either the discount Ellen gets or the actual price Ellen pays. Some proportions may not work for either category. Indicate the letter for each number in your answer sheet. Category from Which to Choose A. Amount of Discount B. Price after Discount C. Neither Discount or Price after Discount Proportion Category y x y 25 x 100 y x y x 0.25x y 125x y 0.25x Discovery Education Techbook Discovery Communications, LLC 8