sat suite question viewer

Algebra / Linear functions 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?

Back question 140 of 152 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

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.