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Algebra / Linear functions Difficulty: Hard

The cost of renting a large canopy tent for up to $10$ days is $dollar sign 430$ for the first day and $dollar sign 215$ for each additional day. Which of the following equations gives the cost $y$ , in dollars, of renting the tent for $x$ days, where $x$ is a positive integer and $x less than or equals 10$ ?

$y = 215 x + 215$

$y = 430 x - 215$

$y = 430 x + 215$

$y = 215 x + 430$

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Explanation

Choice A is correct. It’s given that the cost of renting a large canopy tent is $dollar sign 430$ for the first day and $dollar sign 215$ for each additional day for up to $10$ days. For $x$ days of renting the tent, the cost includes $dollar sign 430$ for the first day and $dollar sign 215$ for each of the $left parenthesis x minus 1 right parenthesis$ additional days. It follows that the cost $y$ , in dollars, of renting the tent can be expressed as $y = 430 + 215 (x - 1)$ , which is equivalent to $y = 430 + 215 x - 215$ , or $y = 215 x + 215$ . Therefore, the equation $y = 215 x + 215$ gives the cost of renting the tent for $x$ days, where $x$ is a positive integer and $x less than or equals 10$ .

Choice B is incorrect. This equation represents a situation where the cost of renting the tent for the first day is $dollar sign 215$ , not $dollar sign 430$ , and the cost for each additional day is $dollar sign 430$ , not $dollar sign 215$ .

Choice C is incorrect. This equation represents a situation where the cost of renting the tent for the first day is $dollar sign 645$ , not $dollar sign 430$ , and the cost for each additional day is $dollar sign 430$ , not $dollar sign 215$ .

Choice D is incorrect. This equation represents a situation where the cost of renting the tent for the first day is $dollar sign 645$ , not $dollar sign 430$ .