Question

Molly and Norachai are selling pies for a school fundraiser. Customers can buy blueberry pies and pumpkin pies. Molly sold 5 blueberry pies and 12 pumpkin pies for a total of $143. Norachai sold 10 blueberry pies and 8 pumpkin pies for a total of $142. Find the cost each of one blueberry pie and one pumpkin pie.

Answer 1

Blueberry costs 9 dollars

Pumpkin costs 7 dollars

Explanation:

Let "b" represent the price of a blueberry pie

Let "p" represent the price of a pumpkin pie

Step 1: Set equation

5b + 12p = 143 ----- 1

10b + 8p = 142 ----- 2

Step 2: Isolate 1 for "b"

5b = 143 - 12p

`b = (143)/(5)-(12)/(5)p` ------- 3

Step 3: Substitute 3 into 2

`10((143)/(5)-(12)/(5) p )+8p=142\\286 - 24p + 8p = 142\\-24p + 8p = 142 - 286\\-16p = -144\\p = -(144)/(-16)\\ p = 9`

Step 4: Subsitute p = 9 into 1 for b

`5p + 12(9) = 143\\5p + 108 = 143\\5p = 143 - 108\\5p = 35\\(5p)/(5)=(35)/(5)\\p = 7`

Therefore a pumpkin pie costs 7 dollars while a blueberry pie costs 9 dollars