SOLUTION: Can you help with this? I'm lost! "Molly's custom kitchen supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork, and $1.30 to buy th

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Can you help with this? I'm lost! "Molly's custom kitchen supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork, and $1.30 to buy th      Log On

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Question 1055067: Can you help with this? I'm lost! "Molly's custom kitchen supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork, and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April they spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks, and how many spoons did they make last April?"
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number of forks they made
Let +b+ = the number of spoons they made
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(1) +1.7a+%2B+1.3b+=+37.9+
(2) +5.6a+%2B+5.4b+=+147.2+
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(1) +17a+%2B+13b+=+379+
(2) +56a+%2B+54b+=+1472+
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(2) +28a+%2B+27b+=+736+
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This is a little tough. I think I will
multiply both sides of (1) by +27+
and both sides of (2) by +13+
Then I'll subtract (2) from (1)
-----------------------------------
(1) +459a+%2B+351b+=+10233+
(2) +-364a+-+351b+=+-9568+
-----------------------------------
+95a+=+665+
+a+=+7+
and
(1) +17a+%2B+13b+=+379+
(1) +17%2A7+%2B+13b+=+379+
(1) +119+%2B+13b+=+379+
(1) +13b+=+260+
(1) +b+=+20+
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They made 7 forks and 20 spoons last April
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check:
(1) +1.7a+%2B+1.3b+=+37.9+
(1) +1.7%2A7+%2B+1.3%2A20+=+37.9+
(1) +11.9+%2B+26+=+37.9+
(1) +37.9+=+37.9+
OK
You can check (2)