CC Investigation 1 Answers to Additional Practice, Skill Practice, and Check-Up

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1 CC Investigation 1 Answers to Investigation 1 Additional Practice 1. a. Calvin s sister would prefer the recipe with the lowest ratio of nuts rather than the lowest amount of nuts. Finding the ratio of nuts to granola for each recipe: A:, B:, C: 7, and D: The lowest ratio is recipe C, so Calvin s sister might prefer that. b. Recipe D; Calvin starts with tablespoons of nuts. Recipe A has a nut-granola ratio of : 1, and recipe D has a ratio of 3 :. For tablespoons of granola, recipe A calls for 1 tablespoons of nuts, so Calvin would need to add 1 = more tablespoons of nuts. For tablespoons of granola, recipe D calls for 9 tablespoons of nuts, so Calvin would need to add 9 = 3 more tablespoons of nuts. 3 <, so Calvin would reach the nut-granola ratio of recipe D first.. a. Distances Driven Distance (mi) y Time (hours) Distance (in mi) Distances Driven x 1 3 Time (h) b. 5 days; Convert the distances to miles: Ottawa to Montreal,. 1 mi; Montreal to Quebec: mi; Quebec to Halifax: 1,. 3 mi. At a speed of 5 mph, Ottawa to Montreal would take h, which is 1 day s drive. Montreal to Quebec would take h, which is 1 day s drive. Quebec to Halifax would take h, which is 3 days drive = 5 days Skill: Write Equivalent Fractions 1. x =. x = 3 3. x = 1. x = 1 5. x = 3. x = 1 7. x =. x = 9. x = 1 1. x = Skill: Find the Unit Rate about about. 19. about $.9/lb. 5.5 mi/h Answers 53

2 CC Investigation 1 Answers to (continued) Investigation 1 Check-Up 1. a. Quinn; Compare the unit rates in minutes per bracelet: Zack: 3 3 = 1 min/bracelet; Tine: 5 5 = 9 min/bracelet; Ernie: = 7 min/bracelet; Quinn: 3 = min/bracelet; b. 1 bracelets; Zack can make min 1 min/bracelet = bracelets in 1 hour. Quinn can make min min/bracelet = 1 bracelets in 1 hour. + 1 = 1 bracelets.. a. Lance; Raul; Convert speeds to mi/h: Marlon:. km/h 1. km/mi mi/h; Bernhard: km/h 1. km/mi 7.5 mi/h. Order the speeds: b. ( ) 3 = = 7.17 mi/h; 7.17 mi/h 1. km/mi 3.5 km/h 3. a. Chocolate chunk: $. 1 cookies = $. per cookie; peanut butter: $. 1 cookies $. per cookie; sugar: $. 1 cookies = $. per cookie b. Chocolate chunk: profit = (1 $.75) (1 $.) = $9.9; peanut butter: profit = (1 $.75) (1 $.) = $.3; sugar: profit = (1 $.75) (1 $.) = $.1. Chocolate chunk generates the most profit per hour. c. Chocolate chunk: 1 1 = 1 hours of sales; 1 $9.9 = $.55. Peanut butter: 1 = 5 hours of sales; 5 $.3 = $31.. Sugar: 3 = 5 1 hours of sales; 5 1 $.1 = $.. Chocolate chunk cookies would generate the greatest profit over hours. d. Yes; Cost per cookie = $.5 1 = $.1. Profit per hour = ( $.75) ( $.1) = $11.. Over hours: = hours of sales; $11. = $7.5 profit. Oatmeal raisin would be more profitable than any other type of cookie. 5 Common Core Teacher s Guide

3 CC Investigation Answers to Investigation Additional Practice 1. a. the length of the rental period b. t c. Bob s: 3t + 9; Cycle Center: 5t d. e. Bob s Bike Rentals; For hours, Cycle Center is cheaper, but for 5 or hours, Bob s is cheaper, so for the greater part of that hour period, Bob s is a better deal.. a. (3.75 ) + (.5 ) = = $3 b. ( ) = () = $3 c. The costs are the same, so the expressions are equivalent. d. Reece s method was easier because adding the prices gave a whole number to multiply, which was easier than multiplying with decimals twice. Skill: Write and Evaluate Expressions 1. 3 n. 3 p 3. s. b + 5. (9) 7 = 3 7 = () = 5 = Bicycle Rental Costs Hours Bob s Cycle Center 1 $1 $5 $15 $1 3 $1 $15 $1 $ 5 $ $5 $7 $3 Skill: Work Backward. 1 songs; $.3 $ = $.3; $.3 $.3 = songs; $1. = $5.1/mo; $5.1 $.3 = songs; $. $.3 = ; + 1 = songs; $ $. = $1.; $1. $.3 = Investigation Check-Up 1. a. 1h, where h represents the number of sections in his History workbook b. 1() = 9 min, or 1. h c. 1(h + p) d. 1h + 1p; The distributive property can be used to show that 1(h + p) = 1h + 1p. e. 1(7 + 11) = 1(1) = 1 min, or 3. h. a d; 19,, 7, b = 17 + d; The commutative property of addition states that a + b = b + a, so d = 1, and Ella has 1 dimes. 3. a. ($.) + 9($.5) b. ($.) + 9($.5) + ($3.) = $1. + $.5 + $1. = $5.5 c. ( ) + (15.5) = 5 + = 11 packages d. 3( $.5), or 3($5.) e. No; $ ($5.) = $5.5 + $15. = $71.5 per group; $71.5 = $9; $9 > $. Answers 55

4 CC Investigation 3 Answers to Investigation 3 Additional Practice 1. a. Tuesday and Wednesday b. Wednesday to Thursday c. Monday: + = ; Tuesday: + = ; Wednesday: = ; Thursday: = ; Friday: 5 = 5; Thursday, Tuesday/Wednesday, Monday, Friday. a. A(, 3); B(, 3); C(, ) b. 1 unit; point B to A = units; point B to C = 3 units; 3 = 1 c. 1 units; P = = 1 3. a. h ; h represents the height in inches to be able to ride the new ride b. 7 9 The closed circle indicates that is part of the solution. c. An infinite number; the arrow points to the right, indicating there is no end to the number of solutions. d. Yes, for example the solution h = 5 does not make sense because no one is 5 inches tall. Skill: Identify Ordered Pairs 1. (1, 3). (, ) 3. (1, ). (3, 1) 5. (1, ). (, 3) 7. (, ). ( 3, ) 9. ( 3, ) 1. ( 3, 3) 11. (3, ) 1. (, 3) Skill: Interpret Graphs of Inequalities 13. x 1. x x x 17. x x 3 Investigation 3 Check-Up 1. a. b. yellow green 3 1 c. yellow and blue d. yellow; blue. a. C 1 blue From biggest loss to biggest gain, the stocks are C, D, A, and B. b. Find the absolute value of each change, and order them from least to greatest: +.5 =.5; = 7.1;.3 =.3;.9 =.9; , so the stocks in order from least to greatest price change are D, A, B, and C. 3. a. Points A and B have the same y-coordinate, 3, but different x-coordinates. Points B and D have the same x-coordinate, but different y-coordinates. Points A and B have coordinates that are opposite integers. b. 1 rotation around the origin, or reflection across the x-axis and a reflection of the image across the y-axis c. 1 units; The other corners of the rectangle would be located at (, 3) and (1, 1); the side lengths are 5, 5,, and.. a. m b The graph shows that any amounts greater than or equal to $ are a solution to the inequality. c D A 1 B red Common Core Teacher s Guide

5 CC Investigation Answers to Investigation Additional Practice 1. a. Skill: Find the Volume 5.,35 in in in yd 3 There are squares and other congruent rectangles. b. No; SA = (5 5) + (1 5) = (5) + (9) = = 1 in. ; c. 1.5 in.; SA = (5 5) + (h 5); 375 = 5 + h;h = 35; h = 1.5. a. Answers will vary. b. V 1 = lwh = 1 = 3 cm 3 ; V = lwh = 7.5 = cm 3 ; V 3 = lwh = 1. 5 = cm 3 ; Comparisons to predictions will vary. c. The third box holds the least amount of tea, so it should cost the least. Skill: Find the Surface Area 1. 1 cm. 1 in m. 3 cm Investigation Check-Up 1. a. 1 in. 1 in. 3 in. 3 in. 15 in. b. Yes; SA = (15 1) + (15 3) + (1 3) = = 59 in. ; 59 <. 3 in. 3 in. Answers 57

6 CC Investigation Answers to (continued). a. 1 in. in. in. 3. a. ft; V = lwh; 3 = 9 h 3 = 5h; h = b. SA = (9 ) + ( ) + (9 ) = = 9 ft. 9 =.15, so she would need 7 cans at a total cost of 7 $5.9 = $37.3. One gallon would cover the area: 35 > 9, at a total cost of $9.99. It is cheaper to buy one gallon.. V = lwh = = 375 ft 3 ; 3 375, so she should build the shed in Exercise 3 because it holds more. in. in. b. 3 boxes; SA = (1 ) + ( ) + ( ) + a b = = 19; 19 = Common Core Teacher s Guide

7 CC Investigation 5 Answers to Investigation 5 Additional Practice 1. a. mean =.; median = 1.5; modes = and 1 b. c. IQR =.5 = 3.5; the data are fairly spread out. d. Most of the values are between and, with a few greater than. e. values:.; 1 values: 1.; values:.; 3 values:.; values: 1.; 5 values:.; values: 3. f. MAD = 1.7; MAD = [(5.) + (5 1.) + (3.) + (1.) + ( 1.) + (.) + ( 3.)] = ( ) = 35. = 1.7 g. The MAD shows the data are fairly spread out.. a. least = ; greatest = 5 b. Intervals: 11, 13, 53, 37; the intervals are equal, and there are few enough that the histogram won t be too big c. Spectator Ages 1 Frequency Age d. Most of the spectators were under years of age. Skill: Finding Mean Absolute Deviation about about 7.. about. 5. about.. about.1 Skill: Reading Box Plots 7. 3,, 5,, 3; range = 7; IQR =. 1,, 7, 1, 1; range = 15; IQR = 9. 5,, 55, 5.5, ; range = 17; IQR = ,, 9, 99, 1; range = ; IQR = 11 Answers 59

8 CC Investigation 5 Answers to (continued) Investigation 5 Check-Up 1. a. mean =.9 in.; median = 5.5 in.; no mode b. c. The IQR is 3 in., so most of the data are clustered around the median. d. Most of the data are clustered around the median, but the minimum value, 57 in., is much less than the rest of the data. e. 57: 7.9; :.9; 5:.1; : 1.1; 7:.1; : 3.1 f. MAD = ( ) 1 = = 1.9 g. Most height are very close to the median height. h. The mean increases from.9 to about 5.; the median increases from 5.5 to ; and there is still no mode.. a. Frequency USA Men s National Team Heights Height (in.) b. The most common height is between 1 and 3 inches, and there are only players shorter than 75 inches tall. 3. a. Frequency 1 USA Women s National Team Heights Height (in.) b. The distribution of heights below 7 inches is fairly even, with most players heights falling between 73 and 75 inches. c. The men s heights overall are greater, and the distribution of heights less even. Common Core Teacher s Guide