Chapter A.8, Problem 57AYU

To determine

To find: What should you price the shirts at initially to ensure this? If, instead of $40\%$ off at the sale, you give $50\%$ off, by how much is your profit reduced?

Answer to Problem 57AYU

Set the original price at 40; there is no profit.

Explanation of Solution

Given:

You are the manager of a clothing store and have just purchased 100 dress shirts for $\$20.00$ each. After 1 month of selling the shirts at the regular price. You plan to have a sale giving $40\%$ off the original selling price. However, you still want to make a profit $\$4$ on each shirt at the sale price.

Calculation:

Selling price $=x$.

Discount $=\frac{40x}{100}$.

Original selling price $x-\frac{40x}{100}$.

Therefore,

$x-\frac{40x}{100}-20=4$

That is $6x-200=40$.

$x=40$

So the $50\%$ off is 20. There is no profit.