Question

A popular fruit drink is made by mixing fruit juices. Such a mixture with 50% juice is to be mixed with another mixture that is 30% juice to get 200 liters of a mixture that is 45% juice. How much of each should be used?

a. 80 liters of 50% juice and 120 liters of 30% juice
b. 100 liters of 50% juice and 100 liters of 30% juice
c. 120 liters of 50% juice and 80 liters of 30% juice
d. 150 liters of 50% juice and 50 liters of 30% juice

Answer 1

To solve the problem, set up a system of equations and solve for the amounts of each mixture that should be used. The correct answer is option a.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's denote the amount of the 50% juice mixture as 'x' and the amount of the 30% juice mixture as 'y'.

We can set up the following equations:

x + y = 200 (since the total volume of the mixture is 200 liters)

0.50x + 0.30y = 0.45(200) (since we want the final mixture to have a juice concentration of 45%)

Solving this system of equations will give us the values of 'x' and 'y', which represent the amounts of each mixture that should be used.

By solving the equations, we find that 'x' = 80 and 'y' = 120. Therefore, the correct answer is option a: 80 liters of 50% juice and 120 liters of 30% juice.