Sean wants to make a mixture that is 50% lemon juice and 50% lime juice.

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

0.5 gallon

1 gallon

2 gallons

2.5 gallons

  2 gallons

Step-by-step explanation:

Let g represent the number of gallons of 100% lemon juice that needs to be in the mix. Then the total amount of lemon juice is ...

  1.00x + 0.30(7 -x) = 0.50(7)

  0.7x +2.1 = 3.5 . . . . . . eliminate parentheses, collect terms

  0.7x = 1.4  . . . . . . . . . . subtract 2.1

  x = 2 . . . . . . . . . . . . . . divide by 0.7

2 gallons of 100% lemon juice should be added to the mixture to make 7 gallons of 50% lemon juice.