how many ounces of 25% apple juice drink and 50% apple juice drink must be mixed to make 50 ounces of 30% apple juice drink?

Question

 how many ounces of 25% apple juice drink and 50% apple juice drink must be mixed to make 50 ounces of 30% apple juice drink?

Answer 1

Let

 

    x = amount of 25% juice

    y = amount of 50% juice

 

    We can construct 2 equations

 

(EQ1)    x + y = 50

(EQ2)   .25x + .50y = .30(x + y)

 

Lets solve the above system using substitution.  Solving for y in the first equation yields

 

           y = 50 - x

 

Substituting into equation 2,

 

           .25x + .50(50 - x) = .30(x + 50 - x)

           .25x + 25 - .50x = .30x + 15 - .30x

           -.25x + 25 = 15

           -.25x = 15 - 25

           -.25x = -10

           -.25x/(-.25) = -10/(-.25)

           x = 40

 

So we need 30 ounces of 25% juice, and 10 ounces of 50% juice