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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 choicesA) 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 + 30Solve for A to get: A = 110
Answer: B