SOLUTION: Two plates and a cup together weigh more than three goblets, whereas two goblets and a cup weigh more than two plates. Does a goblet weigh more or less than two cups? I'm not su

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two plates and a cup together weigh more than three goblets, whereas two goblets and a cup weigh more than two plates. Does a goblet weigh more or less than two cups? I'm not su      Log On


   

Question 170741: Two plates and a cup together weigh more than three goblets, whereas two goblets and a cup weigh more than two plates. Does a goblet weigh more or less than two cups?
I'm not sure how to approach this question... do I assign a variable to each unknown? Or use one variable? Then do I solve using the substitution method or...? I'm lost! help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
OK, first take a deep breath.
Let's get started.
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Name your variables.
G-weight of a goblet
C-weight of a cup
P-weight of a plate
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Next, write down what you know, in mathematical terms.
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"Two plates and a cup together weigh more than three goblets"
1.2%2AP%2BC%3E3G
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"Two goblets and a cup weigh more than two plates"
2.2%2AG%2BC%3E2P
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From 1,
1.2%2AP%2BC%3E3G
2%2AP%3E3G-C
Let's substitute that into equation 2,
2.2%2AG%2BC%3E2P
Now add what we learned above,
2%2AG%2BC%3E2P%3E3G-C
and remove the 2P from the middle,
2%2AG%2BC%3E3G-C
Add C to both sides and subtract 2G fom both sides,
2C%3EG
or
G%3C2C
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A goblet weighs less than two cups.