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Algebra Difficulty: Hard

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 $x less than or equals 10$ ?

$y = 270 x - 135$

$y = 270 x + 135$

$y = 135 x + 270$

$y = 135 x + 135$

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Explanation

Choice D is correct. It's given that 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. Therefore, the cost $y$ , in dollars, for $x$ days, where $x less than or equals 10$ , is the sum of the cost for the first day, $dollar sign 270$ , and the cost for the additional $x minus 1$ days, $dollar sign 135 left parenthesis x minus 1 right parenthesis$ . 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 $dollar sign 135$ for the first day and $dollar sign 270$ 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.