Solution given in a lot of detail so that you can see where everything come from. Used first principles method.
Note that % is like a unit of measurement and it is worth
10% is the same as
50% is the same as
Given that the blend is 5 gallons
Let the amount of drink
Then the amount of drink
The amount of the juice in the blend is 30% so it is 30% of 5 gallons
Don't like decimals so lets get rid of them.
Multiply everything by 10 giving:
Subtract 15 from both sides
Divide both sides by 4
Consider just the LHS:
LHS = RHS so correct