Write and solve a system of equations to determine the price of each type of pie.
Stephanie and Sarah are selling blueberry and blackberry pies for a school fundraiser. Stephanie sold 8 blueberry pies and 1 blackberry pie for a total of $88. Sarah sold 11 blueberry pies and 3 blackberry pies for $147. Find the price of each pie.
Let b represent the price of a blueberry pie and k represent the price of a blackberry pie. We can write the following equations to represent the given information:
8b + k = 88 (Stephanie's sales)
11b + 3k = 147 (Sarah's sales)
Now we can solve this system of equations. We can eliminate k by first multiplying the first equation by 3:
24b + 3k = 264 (Stephanie's sales multiplied by 3)
Now we can subtract Sarah's sales equation from Stephanie's sales equation multiplied by 3
24b + 3k - (11b + 3k) = 264 - 147
13b = 117
b = 9
Now that we know the price of a blueberry pie (b = 9), we can substitute this value back into one of our original equations. Let's use Stephanie's sales equation:
8(9) + k = 88
72 + k = 88
k = 16
So, the price of a blueberry pie is $9 and the price of a blackberry pie is $16.