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When a subscription to a new magazine was purchased for m months, the publisher offered a discount of 75 percent off the regular monthly price of the magazine. If the total value of the discount was equivalent to buying the magazine at its regular monthly price for 27 months, what was the value of m ?

Explanation	Calculations	Help
$We first create variables for the regular monthly price and the subscription length.$	$p = regular monthly price m = number of months for subscription$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the phrase indicating the discount rate.$	$discount per month = \frac{75}{100} \times p = 0.75 p$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We compute the total value of the discount by multiplying the monthly discount by the number of months.$	$total discount = 0.75 p \times m$
$We translate the equivalence between the total discount and the cost of 27 months at full price.$	$0.75 p m = p \times 27$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We isolate m by dividing both sides by p .$	$0.75 p m = 27 p ⟹ 0.75 m = 27$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We solve for by dividing by 0.75 and simplifying the fraction.$	$m = \frac{27}{0.75} = \frac{27}{\frac{3}{4}} = 27 \times \frac{4}{3} = \frac{27 \times 4}{3} = 9 \times 4 = 36$	Theory & Tactics Method Card FDPR2-A Click to view full details

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The solution is m = 36, which corresponds to answer choice D.

When a subscription to a new magazine was purchased for m months, the publisher offered a discount of 75 percent off the regular monthly price of the magazine. If the total value of the discount was equivalent to buying the magazine at its regular monthly price for 27 months, what was the value of m ?

Explanation	Calculations	Help
$We first create variables for the regular monthly price and the subscription length.$	$p = regular monthly price m = number of months for subscription$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the phrase indicating the discount rate.$	$discount per month = \frac{75}{100} \times p = 0.75 p$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We compute the total value of the discount by multiplying the monthly discount by the number of months.$	$total discount = 0.75 p \times m$
$We translate the equivalence between the total discount and the cost of 27 months at full price.$	$0.75 p m = p \times 27$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We isolate m by dividing both sides by p .$	$0.75 p m = 27 p ⟹ 0.75 m = 27$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We solve for by dividing by 0.75 and simplifying the fraction.$	$m = \frac{27}{0.75} = \frac{27}{\frac{3}{4}} = 27 \times \frac{4}{3} = \frac{27 \times 4}{3} = 9 \times 4 = 36$	Theory & Tactics Method Card FDPR2-A Click to view full details

Scroll horizontally to view all columns

The solution is m = 36, which corresponds to answer choice D.