Jennifer and Micaela are selling pies for a school fundraiser. Customers can buy apple pies and pumpkin pies. Jennifer sold 4 apple pies and 5 pumpkin pies for a total of $86. Micaela sold 8 apple pies and 2 pumpkin pies for a total of $92. Find the cost each of one apple pie and one pumpkin pie.

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Step-by-step explanation:

Let 'a' and 'p' stand for the prices of apple and pumpkin pies, respectively. Then the two sales are described by ...

  4a +5p = 86

  8a +2p = 92

Subtract half the second equation from the first to eliminate the 'a' variable.

  (4a +5p) -(1/2)(8a +2p) = (86) -(1/2)(92)

  4p = 40 . . . . . simplify

  p = 10 . . . . . . . divide by 4

Substitute into the first equation:

  4a + 5(10) = 86

  4a = 36 . . . . . subtract 50

  a = 9 . . . . . . . divide by 4

One apple pie costs $9; one pumpkin pie costs $10.

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