A popular fruit drink is made by mixing fruit juices. Such a mixture with 25​% juice is to be mixed with another mixture that is 5​% juice to get 20 liters of a mixture that is 10​% juice. How much of each should be​ used?

Question

Kind of Juice
Number of Liters
Amount of Pure Juice
0.25
x
0.25x
0.05
y
0.1

Answer 1

Let's assume that the amount of the 25% juice mixture to be used is x liters and the amount of the 5% juice mixture to be used is y liters.

The total amount of the mixture is given as 20 liters, so we can set up the equation:
x + y = 20

The amount of pure juice in the 25% juice mixture is 0.25x liters, and the amount of pure juice in the 5% juice mixture is 0.05y liters.

The total amount of pure juice in the mixture is given as 10% of the 20 liters, so we can set up the equation:
0.25x + 0.05y = 0.1(20)

Multiplying both sides of the equation by 100 to eliminate the decimals, we get:
25x + 5y = 10(20)
25x + 5y = 200

Now we have a system of two equations:
x + y = 20
25x + 5y = 200

We can solve this system of equations using substitution, elimination, or matrices. Let's use substitution to find the values of x and y.

From the first equation, we can solve for x:
x = 20 - y

Substituting this value of x into the second equation, we get:
25(20 - y) + 5y = 200
500 - 25y + 5y = 200
-20y = -300
y = 15

Substituting this value of y back into the first equation, we can solve for x:
x + 15 = 20
x = 5

So, we should use 5 liters of the 25% juice mixture and 15 liters of the 5% juice mixture.