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Question 169940: Totally confused! Please help! Many Thanks!
At a local garage sale, Chris bought 4 gardening magazines and 3 mugs for $8.70. Sarah bought 5 magazines, 2 mugs and 3 refrigerator magnets for $12.35. Steve bought 2 magazines, 4 mugs and 4 refrigerator magnets for $15.50. What was the price of each refrigerator magnet?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! At a local garage sale, Chris bought 4 gardening magazines and 3 mugs for $8.70. Sarah bought 5 magazines, 2 mugs and 3 refrigerator magnets for $12.35. Steve bought 2 magazines, 4 mugs and 4 refrigerator magnets for $15.50. What was the price of each refrigerator magnet?
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GM = price of magazines
MU = price of mugs
RM = price of magnets
4GM + 3MU = 870
5GM + 2MU + 3RM = 1235
2GM + 4MU + 4RM = 1550
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It's 3 eqns in 3 unknowns.
There are several ways to solve this. I have an Excel sheet that does determinants, so I'll use that.
| 4 3 0 870 |
| 5 2 3 1235 | = 0
| 2 4 4 1550 |
Det = 4*(8-12) - 3*(20-6) = -16 - 42
Det = -58
Det*GM = 3*(3*1550 - 4*1235) + 870*(2*4-4*3)
Det*GM = 3*(-290) + 870*(-4)
Det*GM = -4350
GM = -4350/(-58)
GM = 75 (cents)
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Sub 75 into the 1st eqn to get MU
4GM + 3MU = 870
300 + 3MU = 870
MU = 190
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Sub GM and MU
2GM + 4MU + 4RM = 1550
150 + 760 + 4RM = 1550
4RM = 640
RM = 160
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Magazine = $0.75
Mug = $1.90
Magnet = $1.60
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