Linear Equations. Additional Options: Hide Multiple Choice Answers (Written Response) Open in Microsoft Word (add page breaks and/or edit questions)

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1 Additional Options: Hide Multiple Choice Answers (Written Response) Open in Microsoft Word (add page breaks and/or edit questions) Copyright 2010 Study Island - All rights reserved. Generation Date: 11/28/2010 Generated By: Margaret Buell 1. Solve for x. Linear Equations 8(x - 3) = -3x + 64 A. x = 8 B. x = 5 C. x = 88 / 5 D. x = 91 / Solve for x. 5(3x - 11) = 45x A. x = -11 / 6 B. x = -2 / 3 C. x = 11 / 6 D. x = 20 / 3 3. Britany pulls into the local convenience store to fill her car up with gas. The 89- octane gas is selling for $2.28 a gallon. She uses the pay at the pump feature and decides to get her car washed for an extra $7.00. What is the total amount of her purchase if she gets 20 gallons of gas? A. $53.60 B. $57.60 C. $52.60 D. $ Forrest Lumber uses the function Page 1 of 10

2 S(t) = -105t to determine the salvage value S(t), in dollars, of a table saw t years after its purchase. How long will it take the saw to depreciate completely? A. 7 years B. 10 years C. 6 years D. 8 years 5. Solve for x. 7(x - 1) = -2x + 83 A. x = 100 / 9 B. x = 18 C. x = 10 D. x = 9 6. Catherine paid $ for an MP3 Player. If the price paid includes a 9% sales tax, which of the following equations can be used to determine the price of the MP3 Player before tax? (Let x represent the cost of the MP3 Player and y represent the total cost after tax) A. y = 1.9x B. y = x + 9x C. y = 1.09x D. y = 0.91x 7. Carson is a salesman at an insurance company. He receives a monthly salary of $ and a $ commission on each policy he sells. If Carson receives his commission check at the end of the month along with his salary check, which of the following equations can be used to determine his total pay for the month. (Let x represent the number of policies sold and y represent the total amount of pay for the month.) A. y = 164x B. y = 16.4x C. y = 933x D. y = 164x Page 2 of 10

3 8. A rental car company charges a base fee of $39.03 plus $0.46 per mile driven. If x represents the number of miles driven, which of the following equations could be used to find y, the total cost of the bill? A. y = $0.46x + $39.03 B. y = $0.76x + $39.03 C. y = $39.49x D. y = $0.46x 9. Larry's Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an average of nine hours per day. The mowing and raking typically takes six hours and an average of forty-five bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill one bag of leaves? A. 5 minutes/bag B. 6 minutes/bag C. 3 minutes/bag D. 4 minutes/bag 10. Mike discovered that the pool in his backyard is leaking slowly. The pool holds 15,253 gallons of water, and is leaking at a rate of 8 gallons per day. If Mike does not replace the water that has leaked from the pool, how many gallons of water will remain in the pool after 94 days? A. 14,877 gallons B. 14,501 gallons C. 15,347 gallons D. 16,005 gallons 11. A company manufactures and sells video games. A survey of video game stores indicated that at a price of $58 each, the demand would be 400 games, and at a price of $28 each, the demand would be 1,300 games. If a linear relationship between price and demand exists, which of the following equations models the price-demand relationship? (Let x represent the price per video game and y represent the demand.) A. B. C. D. Page 3 of 10

4 12. Reid's Hardware discounts all riding lawnmowers 7% to customers paying in cash. If Trey paid $1, in cash for a riding lawnmower, which of the following equations can be used to determine the original price of the lawnmower? (Let x represent the original price of the lawnmower and y represent the discounted price.) A. y = 1.7x B. y = 1.07x C. y = 0.93x D. y = x - 7x 13. LeAnne leaves town traveling at an average speed of 46 mph. After 2 hours, Bart leaves town traveling in the same direction at an average speed of 63 mph. Which of the following equations could be used to represent the distance between LeAnne and Bart after x hours? (Let x represent the time in hours that Bart has been traveling and y represent the distance between LeAnne and Bart.) A. y = 92-63x B. y = 17x C. y = x D. y = 92-17x 14. Solve for x. 6(5x - 3) = 66x A. x = -1 / 2 B. x = 8 / 5 C. x = 14 / 5 D. x = 1 / Forrest Lumber uses the function S(t) = -90t to determine the salvage value S(t), in dollars, of a table saw t years after its purchase. How long will it take the saw to depreciate completely? A. 6 years B. 5 years Page 4 of 10

5 C. 8 years D. 7 years Page 5 of 10

6 Answers 1. A 2. A 3. C 4. D 5. C 6. C 7. A 8. A 9. D 10. B 11. D 12. C 13. D 14. A 15. D Page 6 of 10

7 Explanations 1. Keep in mind that the goal is to isolate x. 8(x - 3) = -3x + 64 Distribute the 8. 8x - 24 = -3x + 64 Add 3x to both sides. 11x - 24 = 64 Add 24 to both sides. 11x = 88 Divide both sides by 11. x = 8 2. Keep in mind that the goal is to isolate x. 5(3x - 11) = 45x Divide both sides by 5. 3x - 11 = 9x Subract 3x from both sides. -11 = 6x Divide both sides by / 6 = x 3. Let y represent the total amount of her purchase and x represent the number of gallons of gas. y(x) = (cost per gallon)x + car wash y(x) = ($2.28/gallon)(x gallons) + $7 Since she purchased 20 gallons of gas, her total purchase costs: y(20) = ($2.28/gallon)(20 gallons) + $7 = $ The saw is completely depreciated when S(t) = 0. So, set S(t) = 0 and solve for t. 0 = -105t t = 840 t = 8 years 5. Keep in mind that the goal is to isolate x. 7(x - 1) = -2x + 83 Distribute the 7. 7x - 7 = -2x + 83 Add 2x to both sides. 9x - 7 = 83 Add 7 to both sides. 9x = 90 Divide both sides by 9. x = 10 Page 7 of 10

8 6. Let x represent the cost of the MP3 Player and y represent the total cost after tax. The total cost of the MP3 Player is equal to the cost of the MP3 Player itself plus the tax. So, total cost = MP3 Player price + tax y = x x y = ( )x y = 1.09x 7. To find the total amount that Carson is paid at the end of the month, add his monthly salary to his commission. Total Pay = (Commission)(# of policies sold) + Salary y = 164x The total bill is equal to the cost per mile driven, $0.46, times the number of miles driven, x, plus the base price, $ Therefore, the linear equation which represents the total rental cost is shown below. y = $0.46x + $ This situation can be represented by a linear equation where the total hours worked is the dependent variable and the hours spent bagging leaves is the independent variable. The raking and mowing is the y-intercept, and the time to bag one bag of leaves is the rate of change, or slope. Use the given information to develop an equation and solve for the slope. 9 hours = m(45 bags) + 6 hours 3 hours = m(45 bags) 3 hours = m(45 bags) 3 hours / 45 bags = m 1 / 15 hours/bag = m It takes 1 / 15 hours, or 4 minutes to bag one bag of leaves. 10. The amount of water in the pool can be modeled by the linear equation V = -8t + 15,253, where V represents the amount of water in the pool and t represents the the time that has passed in days. Evaluate the equation with the given time frame to determine the amount of water in the pool. V = -8(94) + 15,253 gallons V = ,253 gallons V = 14,501 gallons Page 8 of 10

9 11. The problem gives two points and indicates that the price-demand function is linear. Use the two points to find the slope and then the equation of the line passing through the points. So, given the points (58, 400) and (28, 1,300), find the slope, m. Next, use the point-slope form of the equation of a line to find the price-demand function. 12. The discounted price is equal to the original price minus the discount. discounted price = original price - discount y = x x y = (1-0.07)x y = 0.93x 13. First, find the distance that LeAnne has already traveled since she left town. 46 mph 2 hours = 92 miles Next, find the speed at which Bart is approaching LeAnne. 63 mph - 46 mph = 17 mph Next, find an equation that represents the distance between LeAnne and Bart. y = 92-17x 14. Keep in mind that the goal is to isolate x. 6(5x - 3) = 66x Divide both sides by 6. 5x - 3 = 11x Subract 5x from both sides. -3 = 6x Divide both sides by / 2 = x Page 9 of 10

10 15. The saw is completely depreciated when S(t) = 0. So, set S(t) = 0 and solve for t. 0 = -90t t = 630 t = 7 years Copyright 2010 Study Island - All rights reserved. Page 10 of 10