Question

A group of 40 children attended a football game. They either got a hamburger or a hotdog at the concession stand. Hamburgers cost $5 each and hotdogs cost $3 each. The total cost of the hotdogs and hamburgers was $150. How many hamburgers and hotdogs were purchased?

Answer 1

We know that

• There are 40 children.

,

• Hamburgers cost $5 each.

,

• Hotdogs cost $3 each.

,

• The total cost of hotdogs and hamburgers was $150.

Let's call x hamburgers and y hotdogs. The total number of hotdogs and hamburgers is represented by the following equation.

$x+y=40$

The total cost is represented by the following equation.

$5x+3y=150$

Let's multiply the first equation by -3.

$-3x-3y=-120$

Then, we combine it with the second equation.

$\begin{gathered} 5x-3x+3y-3y=150-120 \\ 2x=30 \\ x=\frac{30}{2} \\ x=15 \end{gathered}$

Now we use the x-value to find y.

$\begin{gathered} x+y=40 \\ 15+y=40 \\ y=40-15 \\ y=25 \end{gathered}$

Therefore, there were purchased 15 hamburgers and 25 hotdogs.