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Algebra Difficulty: Hard

The cost of renting a carpet cleaner is $dollar sign 52$ for the first day and $dollar sign 26$ for each additional day. Which of the following functions gives the cost $C (d)$ , in dollars, of renting the carpet cleaner for $d$ days, where $d$ is a positive integer?

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Explanation

Choice A is correct. It's given that the cost of renting a carpet cleaner is $dollar sign 52$ for the first day and $dollar sign 26$ for each additional day. Therefore, the cost $C (d)$ , in dollars, of renting the carpet cleaner for $d$ days is the sum of the cost for the first day, $dollar sign 52$ , and the cost for the additional $d minus 1$ days, $dollar sign 26 left parenthesis d minus 1 right parenthesis$ . It follows that $C (d) = 52 + 26 (d - 1)$ , which is equivalent to $C (d) = 52 + 26 d - 26$ , or $C (d) = 26 d + 26$ .

Choice B is incorrect. This function gives the cost of renting a carpet cleaner for $d$ days if the cost is $dollar sign 78$ , not $dollar sign 52$ , for the first day and $dollar sign 26$ for each additional day.

Choice C is incorrect. This function gives the cost of renting a carpet cleaner for $d$ days if the cost is $dollar sign 26$ , not $dollar sign 52$ , for the first day and $dollar sign 52$ , not $dollar sign 26$ , for each additional day.

Choice D is incorrect. This function gives the cost of renting a carpet cleaner for $d$ days if the cost is $dollar sign 130$ , not $dollar sign 52$ , for the first day and $dollar sign 52$ , not $dollar sign 26$ , for each additional day.