Respuesta :
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:
[tex]10x+8y=102...(1)[/tex]
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:
[tex]4x+12y=98...(2)[/tex]
Now we will use substitution method to solve our system of equations.
Form equation (1), we will get:
[tex]x=\frac{102-8y}{10}[/tex]
Upon substituting this value in equation (2), we will get:
[tex]4(\frac{102-8y}{10})+12y=98[/tex]
[tex]2(\frac{102-8y}{5})+12y=98[/tex]
[tex]\frac{204-16y}{5}+\frac{60y}{5}=98[/tex]
[tex]\frac{204-16y+60y}{5}=98[/tex]
[tex]\frac{204+44y}{5}=98[/tex]
[tex]\frac{204+44y}{5}\cdot 5=98\cdot 5[/tex]
[tex]204+44y=490[/tex]
[tex]204-204+44y=490-204[/tex]
[tex]44y=286[/tex]
[tex]\frac{44y}{44}=\frac{286}{44}[/tex]
[tex]y=6.5[/tex]
Therefore, each bag of popcorn costs $6.5.
