SOLUTION: My daughter and I are stumped on how to set up this equation. I hope we picked the correct topic for this problem... Here's the question: Geno worked at the China Store on Sun

Question 342169: My daughter and I are stumped on how to set up this equation. I hope we picked the correct topic for this problem... Here's the question:
Geno worked at the China Store on Sunday packing dishes for shipment. He received 5 cents for each piece he packed successfully and was fined 12 cents for each piece he broke. If he handled 187 pieces, and was paid $8.16 how many pieces did he break?
We know it's not the correct way to do the problem, but we started by assuming that if he handled all 187 pieces without breaking any, then he would have earned $9.35. Then we started subtracting multiples of .12 to see if we could end up at $8.16. We know there's a correct way to set up the problem but couldn't get it.
Would you please give us as much detail as possible so that we (she) will be able to do similar problems on her own? Thank you so much!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Geno worked at the China Store on Sunday packing dishes for shipment. He received 5 cents for each piece he packed successfully and was fined 12 cents for each piece he broke. If he handled 187 pieces, and was paid $8.16 how many pieces did he break?
We know it's not the correct way to do the problem, but we started by assuming that if he handled all 187 pieces without breaking any, then he would have earned $9.35. Then we started subtracting multiples of .12 to see if we could end up at $8.16. We know there's a correct way to set up the problem but couldn't get it.
---------------------
Your method is the best.
Here's the usual way:
p = # of pieces packed ok
b = # of pieces broken
---------
p + b = 187 (total pieces)
5p - 12b = 816
p = 187 - b (from the 1st eqn)
Sub for p in the 2nd eqn
5(187-b) - 12b = 816
935-5b - 12b = 816
-1b = -119
b = 7
---------
The 2nd method is more work, more chance for error. Yours is better.

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