Create an equation to represent the total amount of money Matt and Phil earned at the fundraiser based on the number of cookies Matt made.

Question

Phil and Matt made cookies for a fundraiser at their high school.

• ​Phil made 25% more cookies than Matt.
• The cookies sold for $0.25 each.
• After the sale, 20% of the combined total of their cookies remained.

​Create an equation to represent the total amount of money Matt and Phil earned at the fundraiser based on the number of cookies Matt made.

Answer 1

If Matt made M cookies then Phil made M+0.25M=1.25M cookies.

Each cookie sells at $0.25 so Phil raised 1.25×0.25M dollars=$0.3125M. That means that if Matt made 100 cookies then Phil would make $31.25. 

Matt and Phil together made M+1.25M=2.25M cookies. If 20% remained after the sale, then they sold 80% of the cookies and made 0.80×0.25×2.25M dollars=0.45M dollars.

So the required equation is S=0.45M dollars, where S is the money raised by the sale of the cookies.

(If Matt made 100 cookies then Phil made 125, and together they made 225 cookies, which would have sold for $56.25. But 20% of the cookies (45 cookies) remained, so they only sold 180 cookies which earned them $45. The equation also confirms this amount when M=100.)