Write and solve a system of equations to determine the cost of one pecan pie and the cost of one apple pie.
Susan and Tony are selling pies for a school fundraiser. The choices are pecan pie or apple pie. Susan sold 13 pecan pies and 9 apple pies for a total of $173. Tony sold 6 pecan pies and 3 apple pies for a total of $66. Find the cost of each pie.
Let x be the cost of one pecan pie and y be the cost of one apple pie. We can write the system of equations as follows:
13x + 9y = 173 (Equation 1: Susan's sales)
6x + 3y = 66 (Equation 2: Tony's sales)
To solve the system of equations, we can use the method of substitution or elimination. In this case, we'll use the elimination method. First, let's multiply Equation 2 by 3 to make the coefficients of y the same in both equations:
18x + 9y = 198 (Equation 2 multiplied by 3)
Now, subtract Equation 1 from the new Equation 2:
18x + 9y - (13x + 9y) = 198 - 173
5x = 25
x = 5
Now that we have the value of x, we can plug it back into either Equation 1 or Equation 2 to solve for y. We'll use Equation 1:
13(5) + 9y = 173
65 + 9y = 173
9y = 108
y = 12
So, the cost of one pecan pie (x) is $5 and the cost of one apple pie (y) is $12.