Question

Sean wants to make a mixture that is 50% lemon juice and 50% lime juice. How much lemon juice should he add to a juice that is 30% lemon juice and 70% lime juice to make 7 gallons 100% of the 50% lemon/50% lime juice mixture?

Answer 1

7 gallons final mixture contains 50% lemon and 50% lime juice.

This means

7 gallons final mixture contains 3.5 gallons lemon and 3.5 gallons lime juice.

Initial mixture contains 30% lemon juice and 70% lime juice .

This means
10 gallons initial mixture contains 3gallons lemon juice and 7gallons lime juice .

So 5 gallons initial mixture contains 1.5 gallons lemon juice and 3.5gallons lime juice .

Hence 2 gallons lemon juice is to be added with this mixture to make the final mixture containing 50% lemon and 50% lime juice.