Question

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 that is 30% lemon juice and 70% lime juice to make 7 gallons of the 50% lemon/50% lime juice mixture?

Answer 1

A.
0.5 gallon

B.
1 gallon

C.
2 gallons

D.
2.5 gallons

Answer 2

p= # of pure lemon juice
m= # of gallons of 30/70 mixture
7= total # of gallons of 50/50 mix
p+m=7

Amount of lemon juice in p gallons of 100% lemon juice = 1p
Amount of lemon juice in m gallons of 30% lemon juice = .3m
Amount of lemon juice in 7 gallons of 50% lemon juice = 3.5
so
p+.3m=3.5

Now solve:
p+m=7
p=7-m

substitute 7-m into second equation for p
(7-m) +.3m=3.5
-.7m=-3.5
m=5

substitute 5 for m into the equation p=7-m
p=7-5
p=2 gallons of 100% lemon juice for wanted results