If a barrel is 1/3 full and then you add 8 gallons to it to make it 3/5ths full, how much does the entire barrel contain?

Make same denoms

1/3 times 5/5=5/15

3/5 times 3/3=9/15

so the question is

5/15 plus 8 gallons=9/15

it take 8 gallons to get from 5 to 9 so

9-5=4

4 units=8 gallons

dividee 4

1unit=2 gallons

entire baralle is 15 units

2*15=30

entire is 30gallons