On a certain day, a bakery produced a batch of rolls at a total production cost of 300 dollars....

Question

On a certain day, a bakery produced a batch of rolls at a total production cost of 300 dollars. On that day, 4/5 of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery's profit on this batch of rolls?

GMAT Panda · Accepted Answer

The bakery’s profit was 132, so the correct answer is C. We let N be the total number of rolls and c the average production cost per roll. c = 300/N We translate "4/5 of the rolls in the batch were sold" into the expression for the rolls sold on day one. 4/5N We express the selling price on day one as 50% greater than the cost per roll. 1.5 c We compute the revenue on day one by multiplying the number of rolls sold by the day one price and substituting for c. R_1 = 4/5N 1.5 c = 4/5N 1.5 300/N = 360 We translate "20 percent less than the price of the day before" into the selling price on day two. p_2 = 0.8 (1.5 c) = 1.2 c We compute the revenue on day two by multiplying the remaining rolls by the day two price and substituting for c. R_2 = 1/5N 1.2 c = 1/5N 1.2 300/N = 72 We find the profit by subtracting the total production cost from the total revenue. Profit = (360 + 72) - 300 = 432 - 300 = 132

Explanation	Calculations	Help
$We let N be the total number of rolls and c the average production cost per roll.$	$c = \frac{300}{N}$
$We translate "4/5 of the rolls in the batch were sold" into the expression for the rolls sold on day one.$	$\frac{4}{5} N$
$We express the selling price on day one as 50% greater than the cost per roll.$	$1.5 \times c$
$We compute the revenue on day one by multiplying the number of rolls sold by the day one price and substituting for c .$	$R_{1} = \frac{4}{5} N \times 1.5 \times c = \frac{4}{5} N \times 1.5 \times \frac{300}{N} = 360$
$We translate "20 percent less than the price of the day before" into the selling price on day two.$	$p_{2} = 0.8 \times (1.5 \times c) = 1.2 \times c$
$We compute the revenue on day two by multiplying the remaining rolls by the day two price and substituting for c .$	$R_{2} = \frac{1}{5} N \times 1.2 \times c = \frac{1}{5} N \times 1.2 \times \frac{300}{N} = 72$
$We find the profit by subtracting the total production cost from the total revenue.$	$Profit = (360 + 72) - 300 = 432 - 300 = 132$

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