Rex Carr could pay $10 for a shovel that lasts one year and pay $5 a car to his brother Scoop to bury the cars, or he could buy a low-quality car smasher that costs $200 a year to own and that smashes cars at a marginal cost of $1 per car.If it were also possible for Rex to buy a high-quality hydraulic car smasher that cost $550 per year to own and if with this smasher he could dispose of cars at a cost of $.67 per car, it would be worthwhile for him to buy this high-quality smasher if he needed to dispose of
A)no more than 525 cars per year.
B)no more than 1,050 cars per year.
C)at least 1,060 cars per year.
D)at least 1,050 cars per year.
E)at least 525 cars per year.

Question

Quizplus · Accepted Answer

First we need to calculate the total cost for each option: Option 1: $10 for shovel + $5 per car for burial = $5x + $15 Option 2: $200 for car smasher + $1 per car for disposal = $200 + $x Option 3: $550 for hydraulic car smasher + $0.67 per car for disposal = $550 + $0.67x We want to know when option 3 is cheaper than option 1 or 2, so we need to set up the inequality: $550 + $0.67x < $5x + $15 AND $550 + $0.67x < $200 + $x Solving each separately: $550 < $4.33x x > 127.165 $550 < $0.33x + $200 $350 < $0.33x x > 1,060.606 The smallest number of cars that satisfies both inequalities is 1,060, so Rex should choose option 3 if he needs to dispose of at least 1,050 cars per year.

Rex Carr Could Pay $10 for a Shovel That Lasts