9514 1404 393
Answer:
30 gallons
Step-by-step explanation:
Let c represent the capacity of the container. Then we have ...
2/5c + 8 = 2/3c
Multiplying by 15 clears the fractions:
6c +120 = 10c
120 = 4c . . . . . . . . subtract 6c
30 = c . . . . . . . . . . divide by 4
The container can hold 30 gallons.
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Additional comment
Often, you are told to "clear fractions" first when solving equations that involve them. Here, you can work directly with the fractions, if you like.
8 = (2/3c) -(2/5c) = 4/15c . . . . . find the difference of the fractions
8(15/4) = c = 30 . . . . . . . . . . . . . multiply by its inverse
