Question

Ava and Greg are selling cookies and popcorn to raise money for a school trip. Ava sold 10 boxes of cookies and 8 bags of popcorn and raised $102. Greg sold 4 boxes of cookies and 12 bags of popcorn and raised $98. How much is a bag of popcorn?

Answer 1

Let x represent number of boxes of cookies and y represent popcorn bags.

We have been given that Ava sold 10 boxes of cookies and 8 bags of popcorn and raised $102. We can represent this information in an equation as:

`10x+8y=102...(1)`

We are also told that Greg sold 4 boxes of cookies and 12 bags of popcorn and raised $98. We can represent this information in an equation as:

`4x+12y=98...(2)`

Now we will use substitution method to solve our system of equations.

Form equation (1), we will get:

`x=(102-8y)/(10)`

Upon substituting this value in equation (2), we will get:

`4((102-8y)/(10))+12y=98`

`2((102-8y)/(5))+12y=98`

`(204-16y)/(5)+(60y)/(5)=98`

`(204-16y+60y)/(5)=98`

`(204+44y)/(5)=98`

`(204+44y)/(5)\cdot 5=98\cdot 5`

`204+44y=490`

`204-204+44y=490-204`

`44y=286`

`(44y)/(44)=(286)/(44)`

`y=6.5`

Therefore, each bag of popcorn costs $6.5.