winter wrote:A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40 percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
1) $40
2) $60
3)$80
4)$90
5)$100

QA is $100

Hi!

We can either set up an equation to solve or we can use the answers to backsolve. Let's try it both ways.

Algebra:

If S = selling price, then:

S(3/5) = 150

(Since the mark-up is 2/5 of selling price, 3/5 of selling price is the original price.)

S = (5/3)(150) = 5*50 = 250

Profit = S - 150 = 250 - 150 = 100

Backsolving:

When we backsolve, start with either (B) or (D). Since it "feels" like the answer should be fairly large, let's start with (D).

Assuming that profit = 90:

S = 150 + 90 = 240

Does 90 = 40% of 240?

.4(240) = 96... nope, so (D) is wrong.

Further, 90 is too high a percent of 240, so we need to use bigger numbers to bring the percent down. Only (E) is bigger than (D), choose (E)!

Since we're having so much fun, let's look at another way we can solve!

Ratios:

We know that 150 is 60% of the selling price and that profit is 40% of the selling price. So:

P/150 = 40/60 = 2/3
P = (2/3)(150) = 100... choose (E)!

Let the markup = x, thus selling price = 150+x

40% of selling price = (40/100) x (150 + x)

This is given to be equal to the markup

x = 40/100 (150+x)

Solve for x to get 100, which is the markup.

Hence, selling price = 150+x = 250
Cost price = 150

Profit = 250-150 = 100