SOLUTION: 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

Question 1207784: 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 of $4 on each shirt at the sale price.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 by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = initial price
0.40x = discount value = amount saved for the customer
x - 0.40x = 0.60x = sale price
0.60x - 20 = profit per shirt = 4 dollars

0.60x - 20 = 4
0.60x = 4+20
0.60x = 24
x = 24/0.60
x = 40
The initial price should be $40.

If that's the case then 40% of $40 = 0.40*40 = 16 dollars is saved and the sale price would be 40-16 = 24 dollars (or 60% of 40 = 0.60*40 = 24).
Then profit per shirt = price-cost = 24-20 = 4 dollars.
We have confirmed $40 is the correct starting price.

Now consider a 50% discount.
The customer saves 0.50*40 = 20 dollars.
The sale price is 40-20 = $20
The profit per shirt is $0 since price-cost = 20-20 = 0.
The manager doesn't gain any money, nor loses money. The manager breaks even.
The old profit $4 dropped to $0, so the profit reduced by $4.

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Summary:

Initial price should be $40
Profit is reduced by $4 if you give a 50% discount instead of a 40% discount.

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