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:

$x=\frac{102-8y}{10}$

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

$4(\frac{102-8y}{10})+12y=98$

$2(\frac{102-8y}{5})+12y=98$

$\frac{204-16y}{5}+\frac{60y}{5}=98$

$\frac{204-16y+60y}{5}=98$

$\frac{204+44y}{5}=98$

$\frac{204+44y}{5}\cdot 5=98\cdot 5$

$204+44y=490$

$204-204+44y=490-204$

$44y=286$

$\frac{44y}{44}=\frac{286}{44}$

$y=6.5$

Therefore, each bag of popcorn costs $6.5.