SOLUTION: One drink contains 5% fruit juice and another contains 50% fruit juice. How many gallons of each type should be combined to make 5 gallons of a drink that contains 40% fruit juice?

Let x be the amount (= the volume) of the 5% fruit juice (in gallons), and
let y be the amount (= the volume) of the 50% fruit juice.


Then you have two equations


     x +      y =     5     gallons   (1)    (the total volume)
0.05*x + 0.50*y = 0.4*5     gallons   (2)    (the volume of the pure juice).


The setup is completed.


To solve the system, I will apply the Substitution method.


For it, express x = 5-y from the first equation and substitute it into the second equation, replacing x. You will get


0.05*(5-y) + 0.5*y = 0.4*5       

0.25 - 0.05y + 0.5y = 2,

0.45y = 2 - 0.25

0.45y = 1.75  ====>  y =  =  =  =  =  =  = .


Answer.   of the 50% fruit juice and the rest   -  =  gallons of the 5% fruit juice.


Check.  Equation (1):   +  = 5.   ! Correct !


        Equation (2):  Left side of the eq. (2) is   +  =  =  = 2 gallons of the pure juice.

                       Right side of the eq(2) is  0.4*5 = 2 gallons of the pure juice.


         Both sides are equal  <-------->  the solution (the answer) is correct !