Question

You are running a concession stand selling hot dogs and sodas. Each hot dog costs $2 and each soda costs $1. At the end of the night, you made a total of $105. You sold a total of 90 hot dogs and sodas combined If x is the number of hot dogs that were sold and y is the number of sodas that were sold, write a system of equations that models this situation.

Answer 1

see the explanation

The number of hot dogs that were sold is 15 and the the number of sodas that were sold is 75

Explanation:

Let

x ---> the number of hot dogs that were sold

y ---> is the number of sodas that were sold

we know that

You sold a total of 90 hot dogs and sodas combined

so

`x+y=90` ----> equation A

You made a total of $105

so

`2x+y=105`

isolate the variable y

`y=105-2x` ----> equation B

substitute equation B in equation A

`x+(105-2x)=90`

solve for x

`x=105-90\\x=15`

Find the value of y (equation B)

`y=105-2(15)=75`

therefore

The number of hot dogs that were sold is 15 and the the number of sodas that were sold is 75