SOLUTION: a bookstore purchased a best selling price at 200 pesos per copy. at what price should this book be sold so that, giving a 20% discount, the profit is 30 %?

Question 159797: a bookstore purchased a best selling price at 200 pesos per copy. at what price should this book be sold so that, giving a 20% discount, the profit is 30 %?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
Cost of the book is 200 pesos.
Profit will be 30% of the cost.
Selling Price will be 20% lower than the retail price.
let C = cost of the book = 200 pesos.
let R = retail price
let S = selling price = retail price minus 20% discount = (R-.2*R) = .8*R
let P = 30% of the cost of the book = 200 * .3 = 60 pesos.
since selling price minus cost = profit, the equation we are looking for becomes
P = S - C
since we know P and C, the equation becomes
60 = S - 200
adding 200 to both sides of the equation and it becomes
60 + 200 = S which becomes
S = 260
since the selling price is 80% of the retail price, we need to solve for the retail price. the equation for the retail price is
.8*R = S
dividing both sides of the equation by .8 and the equation becomes
R = S/.8 = 260 / .8 = 325 pesos.
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we have a solution (retail price is 325 pesos) and we need to prove that it is correct.
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if the retail price is 325 pesos and we provide a discount of 20% on that, then the selling price will be .8 * 325 = 260 pesos.
since the cost is 200, the profit is 60 pesos divided by the cost of 200 pesos yields 30% profit over the cost.
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the solution proves to be correct.
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the answer is:
Retail Price is 325 pesos.
Selling Price is 260 pesos = 80% of Retail Price.
Cost is 200 pesos.
Profit is 60 pesos / Cost = 30%
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