Final answer:
By setting up a system of equations from the sales information, it was determined that the cost of one apple pie is $12 and the cost of one BlackBerry pie is $14.
Step-by-step explanation:
To find the cost of one apple pie and one BlackBerry pie that Amy and Abby are selling for a school fundraiser, we can set up a system of linear equations based on the information given.
Amy sold 12 apple pies and 14 BlackBerry pies for a total of $340. We can represent this as the equation 12a + 14b = 340. Abby sold 12 apple pies and 6 BlackBerry pies for a total of $228, which can be represented as 12a + 6b = 228.
Now, we set up the equations:
- 12a + 14b = 340 (Equation 1)
- 12a + 6b = 228 (Equation 2)
By subtracting Equation 2 from Equation 1, we get 8b = 112. Dividing by 8 yields b = $14. This is the cost of one BlackBerry pie. We can substitute the value of b back into Equation 2 to get 12a + 6(14) = 228, which simplifies to 12a + 84 = 228. Subtracting 84 from both sides, we get 12a = 144, and dividing by 12, we find a = $12. This is the cost of one apple pie.
So, one apple pie costs $12 and one BlackBerry pie costs $14.