SOLUTION: Some students at L.C.V.I. held a bake sale recently to raise money for a field trip. They charged $7 for fruit pies and $10 for meat pies. They sold a total of 52 pies and earn

Question 1170779: Some students at L.C.V.I. held a bake sale
recently to raise money for a field trip.
They charged $7 for fruit pies and $10 for
meat pies. They sold a total of 52 pies and
earned $424. How many of each type of
pie did they sell?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

A setup using formal algebra....

f = # of fruit pies
m = # of meat pies

The total sales, at $7 for each fruit pie and $10 for each meat pie, was $424:

(1)

The total number of pies was 52:

(2)

One possible way to solve this pair of equation is to multiply the second equation by 10 and compare the resulting equation to (1):

(the difference between those two equations)

ANSWER: the number of fruit pies sold was 32; the number of meat pies was 52-32=20.

You can solve the problem informally, using EXACTLY the same calculations, like this:

(1) If all 52 pies were meat pies, the total sales would be $520.
(2) The actual total sales was $424, which is $96 less than $520.
(3) Each fruit pie costs $3 less than each meat pie.
(4) The number of fruit pies sold, to bring the sales total down $96, from $520 to $424, is $96/$3 = 32.

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