1) The combined capacity of a bottle and a glass is equal tothe capacity of a pi

Question

1) The combined capacity of a bottle and a glass is equal tothe capacity of a pitcher. The capacity of abottle is equal to the combined capacity of a glass and amug. The combined capacity of three mugs is equal to thecombined capacity of two pitchers. How many glasses altogether havethe capacity of one mug? a) 3 b) 4 c) 5 d) 6 e) 7 1) The combined capacity of a bottle and a glass is equal tothe capacity of a pitcher. The capacity of abottle is equal to the combined capacity of a glass and amug. The combined capacity of three mugs is equal to thecombined capacity of two pitchers. How many glasses altogether havethe capacity of one mug? a) 3 b) 4 c) 5 d) 6 e) 7

Explanation / Answer

For simplicity, let's label these: p - pitcher b - bottle g - glass m - mug So, we start out with b + g = p. Then we're given that g + m = b,so, in the first equation, replace b by g + m, which gives us theeqn. g + m + g = p which is equal to 2g + m = p Now, at the last, we're given 3m = 2p. Divide both sides to get theeqn. (3/2)m = p. Now we can replace p in the equation above toget: 2g + m = (3/2)m Subtract an m from each side... 2g = (3/2)m - m = (1/2)m And now multiply both sides by 2 to get 4g = m So there you have it. 4 glasses is equal to 1 mug.

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