A school typically sells 500 yearbooks each year for $50 each. The economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. The revenue for yearbook sales is equal to the number of yearbook sold times the price of the yearbook. Let x represent the number of $5 decreases in price. If the expression that represents the revenue is in the form R(x)=(500+ax)(50-bx). Find the values of a and b.

Question

a=100
b=5

show how to get this answer in short steps

Answer 1

1. Revenue is equal to the number of yearbooks sold times the price of the yearbook. Therefore, the revenue equation is R(x) = (500 + ax)(50 - bx).

2. Given that for every $5 decrease in price, the school can sell 100 more yearbooks. This means that a = 100 and b = 5.

3. Plug in the values of a and b into the revenue equation: R(x) = (500 + 100x)(50 - 5x).

4. Simplify the equation: R(x) = (500 + 100x)(50 - 5x) = 500(50 - 5x) + 100x(50 - 5x) = 25000 - 2500x + 5000x - 500x^2.

5. Combine like terms and simplify further: R(x) = 25000 + 2500x - 500x^2.

6. So, the values of a and b are a = 100 and b = 5.