SOLUTION: Thomas bakes pies for a local caterer. On Tuesday he made three peach pies and six cherry pies, costing him $48 in expenses. Friday he spent $54.50 to make seven peach and four che

Question 1173873: Thomas bakes pies for a local caterer. On Tuesday he made three peach pies and six cherry pies, costing him $48 in expenses. Friday he spent $54.50 to make seven peach and four cherry pies. What is the cost of each peach and each cherry pie?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

by formal algebra....

3p+6c=48.00
7p+4c=54.50

Multiply the first equation by 2 and the second by 3 to make the numbers of cherry pies the same; then compare the two resulting equations to determine the cost of each peach pie. Then use that to determine the cost of each cherry pie.

Informally (good practice in problem solving, using logical reasoning and simple mental arithmetic)....

3 peach and 6 cherry for $48 --> 1 peach and 2 cherry for $16 --> 2 peach and 4 cherry for $32.

2 peach and 4 cherry for $32, and 7 peach and 4 cherry for $54.50, --> 5 peach for $54.50-$32=$22.50 --> 1 peach for $22.50/5 = $4.50.

1 peach and 2 cherry for $16, and 1 peach for $4.50, means 2 cherry for $11.50, so 1 cherry for $11.50/2 = $5.75.

ANSWERS: peach $4.50; cherry $5.75

CHECK:
3(4.50)+6(5.75) = 13.50+34.50 = 48
7(4.50)+4(5.75) = 31.50+23 = 54.50

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