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.

Question

Let x represent the number of $5 decreases in price. If the expression that represents the revenue is written in the form R(x) = (500+ ax) (50-bx). Find the values of a and b.

a=
b=

Answer 1

To find the values of a and b, we need to consider the information given in the question.

From the information given, we know that for every $5 decrease in price, the school can sell an additional 100 yearbooks. This means that the total number of yearbooks sold is 500 + 100x, where x represents the number of $5 decreases in price.

Given that the price per yearbook decreases by $5 for each x, the price per yearbook is then $50 - 5x.

Therefore, the revenue, R(x), is equal to the number of yearbooks sold times the price of the yearbook, which can be expressed as:

R(x) = (500 + 100x)(50 - 5x)
= 500(50 - 5x) + 100x(50 - 5x)
= 25000 - 2500x + 5000x - 500x^2
= 25000 + 2500x - 500x^2

Comparing this with the given form R(x) = (500 + ax)(50 - bx), we find that a=2500 and b=500.

Therefore, a=2500 and b=500.