Problem Solving

Vincen wrote: ↑

Mon Oct 19, 2020 9:09 am

Jennifer can buy watches at a price of \(B\) dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of \(T\) by selling \(N\) watches, then in terms of \(B\) and \(T\) and \(N,\) what is the percent of the markup from her buy price to her sell price?

A. \(\dfrac{100T}{NB}\)

B. \(\dfrac{TB}{100N}\)

C. \(\dfrac{100TN}{B}\)

D. \(\dfrac{\frac{T}{N} - B}{100B}\)

E. \(\dfrac{100(T - NB)}{N}\)

Answer: A

Solution:

The profit (or markup) per watch is T/N. So the markup is:

[(T/N)/B] x 100 = 100T/(NB)

percent of the purchase price.

Alternate Solution:

Jennifer’s profit per watch is T/N. Using the formula for profit, we can compute Jennifer’s sell price:

profit = sell price – buy price

T/N = sell price – B

T/N + B = sell price

We now use the percent markup formula:

% markup = [(Sell price – Buy price) / Buy price] x 100

% markup = [(T/N + B – B) / B] x 100

% markup = [(T/N) / B] x 100

% markup = [T/BN] x 100

% markup = 100T / (BN)

Answer: A