James paid 80 cents for each souvenir program that he bought at the Super Bowl game last Sunday. He sold all but 20 of them for $1.50 and made a profit of $54. How many programs did he buy?

Answer 1

The best way to tackle this question is by creating an equation that we can solve to find x, which will be our number of programs.

We can start by setting the equation equal to the amount of money that James made, which is $54. We can set that amount equal to the money James earned from the programs he sold, which would be 1.5*(x-20). We subtract 20 from x because we know that James was unable to sell 20 of his programs. Adding in the cost of purchasing the programs, our equation becomes $54 = 1.5(x-20) - .8(x). The .8 represents the cost of each program, and x is the number of programs purchased.

Solving for x, we get:

$54 = 1.5x - 30 - .8x

$54 = .7x - 30

$84 = .7x

x = $84/.7

x = 120 programs