How many apple pies did Susan buy?

Two varieties of pies are available at a fruit stand. Apple pies cost $5.75 each and cherry pies cost $6.50 each. Susan bought nine pies for a total cost of $53.25.  There is no tax charged. 
​How many apple pies did Susan buy?

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Set up a system of two equations.  One equation will show the number of pies bought, and the other equation will involve the prices.

a = number of apple pies
c = number of cherry pies

a + c = 9   {Susan bought a total of nine pies}
5.75a + 6.5c = 53.25   {each apple pie costs $5.75 and each cherry pie costs $6.50}

Use the substitution method by solving the first equation for a, and then substituting in.

a + c = 9   {first equation}
a = -c + 9   {subtracted c from each side of first equation}

Substitute (-c + 9), in for a, into second equation}

5.75a + 6.5c = 53.25   {second equation}
5.75(-c + 9) + 6.5c = 53.25   {substituted (-c + 9) in for a into second equation}
-5.75c + 51.75 + 6.5c = 53.25   {used distributive property}
0.75c + 51.75 = 53.25   {combined like terms}
0.75c = 1.5   {subtracted 51.75 from each side}
c = 2   {divided each side by 0.75}

Susan bought 2 cherry pies.  Determine the number of apple pies by substituting 2, in for c, into the 
equation a = -c + 9.

a = -c + 9   
a = -2 + 9   {substituted 2 in for c}
a = 7   {added}

Susan bought 7 apple pies.

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