A marketer bought \(N\) crates of empty cardboard gift boxes

[AAPL]

Magoosh

A marketer bought \(N\) crates of empty cardboard gift boxes. Each crate held \(Q\) individual gift boxes, and the lot of \(N\) crates was purchased at a wholesale price of \(W\) dollars. This marketer will sell collections of \(J\) cardboard gift boxes to retailers, at a price of \(P\) dollars for each collection. (Note: \(J\) is a divisor of \(Q\)). The marketer knows that when he has sold all the cardboard gift boxes this way, he wants to net a total profit of \(Z\) dollars on the entire transaction. What price \(P\) must he charge, to net this profit? Express \(P\) in terms of \(N, Q, W, J\), and \(Z\).

A. \(\frac{J(Z - W)}{NQ}\)

B. \(\frac{J(Z + W)}{NQ}\)

C. \(\frac{Q(Z - W)}{NJ}\)

D. \(\frac{Q(Z + W)}{NJ}\)

E. \(\frac{N(Z - W)}{QJ}\)

OA B

[Ian Stewart]

The person bought NQ boxes in total, then packaged sets of J boxes together, so sold a total of NQ/J sets. If those sold for P dollars each, the revenue was PNQ/J dollars. The profit was the revenue minus the expense, W, so the profit Z is given by:

Z = PNQ/J - W

We need to solve for P:

Z+W = PNQ/J
J(Z+W) = PNQ
J(Z+W)/NQ = P

which is answer B.