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BrentGMATPrepNow
Barrel A and barrel B have a combined capacity of 360 liters. If barrel B's capacity is 30 liters greater than twice barrel A's capacity, what is the capacity of barrel A?

A) 90
B) 110
C) 120
D) 130
E) 165

Aside: There are several ways to solve this question. See how many different solutions you can find.

APPROACH #1: Test the answer choices

A) 90
If barrel A holds 90 liters, then barrel B's capacity = 2(90) + 30 = 210 (since we're told B's capacity is 30 liters greater than twice A's capacity)
So, barrel B holds 210 liters, which means their COMBINED capacity = 90 + 210 = 300 liters.
So, answer choice A is wrong since we're told their combined capacity is 360 liters.

B) 110
If barrel A holds 110 liters, then barrel B's capacity = 2(110) + 30 = 240 (since we're told B's capacity is 30 liters greater than twice A's capacity)
So, barrel B holds 250 liters, which means their COMBINED capacity = 110 + 250 = 360 liters.
Bingo!
Answer: B


APPROACH #2: 1 variable
Let x = barrel A's capacity (I chose this quantity since the questions is explicitly asking for this value)
So, 360 - x = barrel B's capacity (since the two barrels have a combined capacity of 360 liters)

If barrel B's capacity is 30 liters greater than twice barrel A's capacity, we can write: 360 - x = 2x + 30
Add x to both sides: 360 = 3x + 30
Subtract 30 from both sides: 330 = 3x
Solve: x = 110
Answer: B


APPROACH #3: 2 variables
Let A = barrel A's capacity
Let B = barrel B's capacity
Since they have a combined capacity of 360 liters, we can write: A + B = 360
Since barrel B's capacity is 30 liters greater than twice barrel A's capacity, we can write: B = 2A + 30

We now have the following system of equations:
A + B = 360
B = 2A + 30

Solve for A to get: A = 110
Answer: B
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