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.

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9ca5r82 9ca5r82 · Answer 1 · 2020-08-14T21:33:44+02:00

Answer:

Blueberry costs 9 dollars

Pumpkin costs 7 dollars

Step-by-step 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

[tex]b = \frac{143}{5}-\frac{12}{5}p[/tex] ------- 3

Step 3: Substitute 3 into 2

[tex]10(\frac{143}{5}-\frac{12}{5} p )+8p=142\\286 - 24p + 8p = 142\\-24p + 8p = 142 - 286\\-16p = -144\\p = -\frac{144}{-16}\\ p = 9[/tex]

Step 4: Subsitute p = 9 into 1 for b

[tex]5p + 12(9) = 143\\5p + 108 = 143\\5p = 143 - 108\\5p = 35\\\frac{5p}{5}=\frac{35}{5}\\p = 7[/tex]

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