Problem Solving

BTGmoderatorLU wrote: ↑

Sat Oct 08, 2022 5:45 pm

Source: Magoosh

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

The OA is 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