Question 213151: A large bucket holds 3 liters more than twice as much as a small bucket. It took 2 small bucket and 5 large buckets to fill a 63 liter tank. How much does a large bucket hold?
Answer by gypsy1274(9)   (Show Source):
You can put this solution on YOUR website! Let x = small bucket and y = large bucket.
- 2 small buckets and 5 large buckets fill a 63 liter tank
2x + 5y = 63
- A large bucket holds 3 liters more than twice as much as a small bucket.
y = 2x + 3
y is already solved in terms of x. If it wasn't, that would be your first step.
Replace all occurrences of y with the solution in the second equation that is already solved for y.
2x + 5(2x+3) = 63
Order of Operations determines the next action. Remove the parenthesis around the 2x+3 by distributing the 5.
2x + 10x + 15 = 63
Combine like terms: add 2x + 10x.
12x + 15 = 63
The goal is to get x by itself so subtract 15 from both sides.
12x = 48
Now divide both sides by 12.
x = 4
Now, since x = the small bucket = 4, we can figure out the size of the large bucket by returning to the second equation.
y = 2x + 3
Plug 4 in for x and solve for y.
y = 2(4) + 3
y = 8 + 3
y = 11
Always check your work.
It took 2 small buckets (4 liters) and 5 large buckets (11 liters) to fill a 63 liter tank.
2(4) + 5(11) = 63
8 + 55 = 63
63 = 63
The answers are correct.
Go back to the original problem to make sure you are answering the correct question.
How much does a large bucket hold?
The large bucket holds 11 liters.
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