Percent application problem

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.

Part A
Create an equation to represent the total amount of money that Matt and Phil earned at the fundraiser based on the number of cookies Matt made.  Explain how you determined your equation.

Part C
Next year Phil and Matt may sell the cookies for $0.50 each. They plan to make the same total number of cookies, but they predict that they will only sell 70% of them given the price increase. Based on their prediction, should Phil and Matt raise the price of the cookies? Justify your answer.

Part B
Phil and Matt made a total of $72.00 selling the cookies.  How many cookies did Phil make and how many cookies did Matt make?  Show your work.

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Part A
x = number of cookies Matt made
1.25x = number of cookies Phil made   {Phil made 25% more cookies than Matt}
A = total money earned

A = (0.25)(0.8)(x + 1.25x)  

They sold 80% of the combined cookies made at $0.25 each.

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Part B
From Part A
x = number of cookies Matt made
1.25x = number of cookies Phil made   {Phil made 25% more cookies than Matt}
A = total money earned

A = (0.25)(0.8)(x + 1.25x)   {created equation from Part A}
72 = 0.25(0.8)(x + 1.25x)   {substituted 72 in for A, the total earned}
72 = 0.2(2.25x)   {multiplied and combined like terms}
72 = 0.45x   {multiplied}
x = 160   {divided each side by 0.45}
Matt made 160 cookies

1.25x   {represents the number of cookies Phil made}
= 1.25(160)   {substituted 160, in for x, into 1.25x}
= 200   {multiplied}
Phil made 200 cookies

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Part C
This year, they made 360 cookies, selling 80% (288 cookies) at $0.25 each,
which produced a total amount earned of $72.00.

Next year, the are selling each for $0.50. They predict they will only need to sell 70% of the cookies.

70% of 360 cookies sold at $0.50 each
= 360(0.7)(0.5) {multiplied cookies by percent sold by price each}
= $126 {multiplied}

Selling 70% of the 360 cookies at $0.50 each, instead of 80% of the 360 cookies at $0.25 each, will raise the income by $54.

They should raise the price.

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