Question

Jake’s Cameras purchased a digital camera at a wholesale cost of $80. They marked up the price 50 percent above the wholesale cost to use as their selling price. After every month that the camera didn’t sell, the store reduced the selling price by 25 percent. After how many monthly price reductions did the price dip below the wholesale cost?

Answer 1

2 months

Explanation:

Answer 2

3 months

Explanation:

Wholesale price was $80. A 50% markup would be $40, and so the initial price after markup would be 1.50($80) = $120.

From this point on we're working with a geometric progression in which the common ratio is (1.00 - 0.25), or 0.75 and each term is 0.75 times the previous term. Here the original wholesale cost) is $80. After how many months will $120*0.75^(n -1) equal $80 or dip below $80?

Let's solve $120*0.75^(n -1) ≤ $80:

Dividing both sides by $80 yields 1.5*0.75^(n - 1) ≤ 1. Using rules of exponents and logs, this transforms into:

log 1.5 + (n - 1)log 0.75 ≤ log 1 (which is zero).

Then log 1.5 + (n - 1)log 0.75 ≤ 0, or

0.1761 + (n - 1)(-0.1249) ≤ 0. Rearranging this yields

(n - 1)(0.1249) = 0.1761, so that

(n - 1) = 0.1761/0.1249, or

n - 1 = 1.410, so that n = 2.410

This tells us that the price will drop to $80 or below after 2.4 months. Let's round that up to 3: 3 months.