SOLUTION: A farm store sells apple pies and apple sauce. 5 Granny Smith apples and 3 Golden Delicious apples are needed to bake a pie. 4 Granny Smith apples and 2 Golden Delicious are needed

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A farm store sells apple pies and apple sauce. 5 Granny Smith apples and 3 Golden Delicious apples are needed to bake a pie. 4 Granny Smith apples and 2 Golden Delicious are needed      Log On


   



Question 1056452: A farm store sells apple pies and apple sauce. 5 Granny Smith apples and 3 Golden Delicious apples are needed to bake a pie. 4 Granny Smith apples and 2 Golden Delicious are needed to make applesauce. If 169 Granny Smith apples and 95 apples were picked on the farm, then how many apple pies "p" and batches of applesauce "a" can be made if every apple is used? Write and solve a system of equations.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I am reading this right:
(1) +5p+%2B+4a+=+169+
(2) +3p+%2B+2a+=+95+
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Multiply both sides of (2) by +2
and subtract (1) from (2)
(2) +6p+%2B+4a+=+190+
(1) +-5p+-+4a+=+-169+
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+p+=+21+
and
(2) +3%2A21+%2B+2a+=+95+
(2) +63+%2B+2a+=+95+
(2) +2a+=+32+
(2) +a+=+16+
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21 pies and 16 batches of applesauce can be made
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check:
(1) +5p+%2B+4a+=+169+
(1) +5%2A21+%2B+4%2A16+=+169+
(1) +105+%2B+64+=+169+
(1) +169+=+169+
OK