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If a bottle and a glass balance with a pitcher, a bottle balances with a glass and a plate, and two pitchers balance with three plates,
can you figure out how many glasses will balance with a bottle?
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Yes I can.
Let b = mass of bottle;
g = mass of glass;
p = mass of pitcher;
L = mass of plate.
Then from the condition, you have these 3 equations for 4 variables:
b + g = p, (1)
b = g + L, (2)
2p = 3L. (3)
From (1) and (3) you have
b + g = . (4)
From (2) you have
L = b - g. (5)
Substitute (5) into (4) replacing and eliminating L. You will get
b + g = . (6)
Simplify (6):
2b + 2g = 3b - 3g ---> 5g = b.
Answer. 5 glasses balance 1 bottle.
Solved.