Find the number of hot dogs and the number of sodas they sold.

Question

At the concession stands at the football game, hot dogs are $1.50 and sodas are $0.50. During one Friday night, the concession stand sold a total of 87 hot dogs and sodas for $78.50. Find the number of hot dogs and the number of sodas they sold.

Answer 1

The solution to this problem requires two equations.

 

First let x= the number of hot dogs, and y = the number of sodas

Then $1.50x + $0.50y = $78.50

 

Second, we know that x + y = 87

 

We then solve the second equation for x, which is x = 87 - y

 

We substitute that value into the first equation, which gives us

$1.50(87 - y) + $0.50y = $78.50;

we get $130.5 - $1.50y + $0.50y = $78.50; after we combine all the factors, we get y = 52

substituting that value into equation 2, we get x = 35

 

So, x = 35 and y = 52

 

Checking our work using the first equation,

$1.50(35) + $0.50(52) = $78.50