Two small buckets and one large bucket can hold 8 cups of gasoline. One large bucket minus one small bucket constitutes 2 cups of gasoline. How many cups of gasoline can each bucket hold?

Question

How many cups of gasoline can each bucket hold?

Answer 1

Let:

Bs = bucket small

Bl = bucket large

Right the equations given to you via problem statement:

2Bs + 1Bl = 8 cups (1)

1Bl - 1Bs = 2 cups (2)

You now have a system of 2 equations and 2 unknowns:

Take (2) and solve for Bl:

1Bl = 2 cups + 1Bs (3) (added 1Bs from one side to the other)

now put this new equation, (3), back into equation (1):

2Bs + 2 cups + 1Bs = 8 cups

3Bs = 6 cups (now divide 2 by each side)

Bs = 2 cups (ANSWER!)

Now put that answer back into equation (3) to get the cups per large bucket:

1Bl = 2 cups + 1Bs

1Bl = 2 cups + 2 cups

1Bl = 4 cups (ANSWER!)

Answer 2

2s + l = 8

l - s = 2

Subtract bottom from top

3s = 6

s = 2