The cost of renting a backhoe for up to 10 days is $ 270 for the first day and $

Question

The cost of renting a backhoe for up to $10$ days is $dollar sign 270$ for the first day and $dollar sign 135$ for each additional day. Which of the following equations gives the cost $y$ , in dollars, of renting the backhoe for $x$ days, where $x$ is a positive integer and $x less than or equals 10$ ?

A.

$y = 270 x - 135$

B.

$y = 270 x + 135$

C.

$y = 135 x + 270$

D.

$y = 135 x + 135$

Accepted Answer

Choice D is correct. It's given that the cost of renting a backhoe for up to 10 days is $ 270 for the first day and $ 135 for each additional day. Therefore, the cost y , in dollars, for x days, where x &#8804; 10 , is the sum of the cost for the first day, $ 270 , and the cost for the additional x - 1 days, $ 135 x - 1 . It follows that y = 270 + 135 x - 1 , which is equivalent to y = 270 + 135 x - 135 , or y = 135 x + 135 . Choice A is incorrect. This equation represents a situation where the cost of renting a backhoe is $ 135 for the first day and $ 270 for each additional day. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

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