SOLUTION: A department store sells 20 portable stereos per week at $80 each. The manager believes that for each decrease of $5 in the price, six more stereos will be sold. What price should

Question 1121171: A department store sells 20 portable stereos per week at $80 each. The manager believes that for each decrease of $5 in the price, six more stereos will be sold. What price should be charged if the revenue needs to be $2240?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
If n counts each $5 increment

PRICE QUANTITY SOLD 80 20 80-5 20+6 80-2*5 20+2*6 80-3*5 20+3*6 . . 80-5n 20+6n

Revenue to be $2240,

Simplify and solve.
n is how many $5 increments to remove from $80.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

The condition says that at the price (80 - 5x) dollars for one stereo the number of stereos sold will be (20 + 6x), where x is an integer number. Then the problem ask to find "x" in such a way that (80-5x)*(20+6x) = 2240. 1600 - 100x + 480x - 30x^2 = 2240 - 30x^2 + 380x - 640 = 0 3x^2 - 38x + 64 = 0 = = . Only positive integer root makes sense, which is x= 2. Answer. The price under the question is (80-5x) = 80 - 5*2 = 70 dollars.

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