SOLUTION: There are two barrels, one containing 40 gallons of wine and 60 gallons of water, the other containing 70 gallons of wine and 30 gallons of water.A pailful is taken from the first
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Question 1130483: There are two barrels, one containing 40 gallons of wine and 60 gallons of water, the other containing 70 gallons of wine and 30 gallons of water.A pailful is taken from the first barrel and poured into the second. After mixing, a pailful is poured back into the first barrel. The proportions of wine to water in the first barrel are now 19:26. What is the capacity of the pail?
Choices: a. 8 b. 10 c. 12 d. 14 Answer by greenestamps(13203) (Show Source):
Barrel A initially contains 40 gallons of wine and 60 gallons of water; barrel B initially contains 70 gallons of wine and 30 gallons of water.
When the pail is filled from barrel A, the ratio of wine to water in the pail is 40:60, so what is in the pail is 0.4x gallons of wine and 0.6x gallons of water.
Barrel A is now left with gallons of wine and gallons of water.
When the pail is emptied into barrel B, barrel B now contains gallons of wine and gallons of water.
The fraction of barrel B that is wine is now ; the fraction that is water is now .
When the pail is now filled from barrel B, the amounts of wine and water in the pail are
wine:
water:
When the pail is emptied into barrel A, the amounts of wine and water in the barrel are
wine:
water:
The ratio of wine to water in barrel A is now 19:26, so
I wouldn't even think of solving that equation algebraically. My graphing calculator did it quite easily. See if yours will too.
The answer is indeed one of the given answer choices.
