A school typically sells 500 yearbooks in a year for $50.00 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 written in the form R(x) = (500 + ax)(50-bx). Find the values of a and b.
First, let's use the information given to create an equation for the number of yearbooks sold as a function of the price decrease.
Let's say the original price is $50 and the number of yearbooks sold is 500. If the price decrease is $5x, then the new price will be $50 - $5x. Using the information that for every $5 decrease in price, 100 more yearbooks are sold, we get the equation for the number of yearbooks sold as:
Yearbooks sold = 500 + 100x
Now we can create the equation for revenue as a function of x:
R(x) = (500 + 100x)(50 - 5x)
R(x) = (500 + 100x)(50) - (500 + 100x)(5x)
R(x) = 25000 + 5000x - 2500x - 500x^2
R(x) = -500x^2 + 2500x + 25000
Comparing this with the form R(x) = (500 + ax)(50 - bx), we can find the values of a and b.
a = 100
b = 5
Therefore, the values of a and b are a = 100 and b = 5.