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Suppose that a bottle and a glass balance with a pitcher. A bottle balances a glass and a plate. T.wo pitchers balance with three plates How many glasses are needed to balance with a bottle?
Swoofter
Where:
- b ≡ bottle
- g ≡ glass
- p ≡ pitcher
- L ≡ plate
Then we are told:
- b + g = p
- b = g + L
- 2p = 3L
First, we need to eliminate the term L from our second equation. We'll start by taking the third equation, solving it for L, then plugging it into the second one:
2p = 3L
∴ L = 2p/3
b = g + L
∴ b = g + 2p/3
then solve it for p:
∴ b - g = 2p/3
∴ 3(b - g)/2 = p
Now we have two equations for p in terms of b and g. Because both expressions are equal to p, we know then that they are equal to each other, so we can say:
3(b - g)/2 = b + g
Now we can solve for b:
∴ 3b - 3g = 2b + 2g
∴ 3b - 2b = 2g + 3g
∴ b = 5g
And that gives us our answer. One "b", or bottle, is equal to 5 "g"'s or glasses, so the answer to the question is five.
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∙ 14y ago
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