When a subscription to a new magazine was purchased for m...

Question

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 ?

GMAT Panda · Accepted Answer

The solution is m = 36, which corresponds to answer choice D. We first create variables for the regular monthly price and the subscription length. p = regular monthly price m = number of months for subscription We translate the phrase indicating the discount rate. discount per month = 75/100 p = 0.75p We compute the total value of the discount by multiplying the monthly discount by the number of months. total discount = 0.75p m We translate the equivalence between the total discount and the cost of 27 months at full price. 0.75p m = p 27 We isolate m by dividing both sides by p. 0.75pm = 27p 0.75m = 27 We solve for m by dividing by 0.75 and simplifying the fraction. m = 27/0.75 = 273/4 = 27 4/3 = 27 43 = 9 4 = 36

Explanation	Calculations	Help
$We first create variables for the regular monthly price and the subscription length.$	$p = regular monthly price m = number of months for subscription$
$We translate the phrase indicating the discount rate.$	$discount per month = \frac{75}{100} \times p = 0.75 p$
$We compute the total value of the discount by multiplying the monthly discount by the number of months.$	$total discount = 0.75 p \times m$
$We translate the equivalence between the total discount and the cost of 27 months at full price.$	$0.75 p m = p \times 27$
$We isolate m by dividing both sides by p .$	$0.75 p m = 27 p ⟹ 0.75 m = 27$
$We solve for by dividing by 0.75 and simplifying the fraction.$	$m = \frac{27}{0.75} = \frac{27}{\frac{3}{4}} = 27 \times \frac{4}{3} = \frac{27 \times 4}{3} = 9 \times 4 = 36$

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