Question

Sam sells hamburgers and cheeseburgers at the concession stand every weekend. Hamburgerscost $2.00 and cheeseburgers cost $2.50. He sold a total of 17 hamburgers and cheeseburgers onFriday night and made $39. How many cheeseburgers did Sam sell?

Answer 1

Given:

The cost of a hamburgers, h=$2.0.

The cost of a cheeseburgers, c=$2.50.

The total number of burgers sold, n=17.

The amount made by Sam by selling burgers, A=$39.

Let x be the number of hamburgers sold and y be the number of cheeseburgers sold.

The expression for the number of burgers is,

`\begin{gathered} n=x+y \\ 17=x+y------(1) \end{gathered}`

The expression for the amount made by Sam by selling burgers is,

`\begin{gathered} A=hx+cy \\ 39=2x+2.5y-----(2) \end{gathered}`

Multiply equation (1) by 2.

`34=2x+2y\text{ -------(3)}`

Subtract equation (3) from (2) to obtain the value of y.

`\begin{gathered} 39-34=2.5y-2y \\ 5=0.5y \\ (5)/(0.5)=y \\ 10=y \end{gathered}`

Therefore, the number of cheese burgers sold by Sam is 10.