linear equation

Question

One canned juice drink is 20% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 15L that is 19% orange juice?

 

How many liters of the 20% orange juice should be in the picture?

Answer 1

Let x = liters of 20% orange juice. Then 15 - x = liters of 5% orange juice (since we want 15 liters altogether).

 

The amount of orange juice in the 20% drink is 0.2x. The amount of orange juice in the 5% drink is 0.05(15 - x) = 0.75 - 0.05x. We want a total of 0.19(15) = 2.85 liters of orange juice in the final drink. So:

 

(orange juice in first drink) + (orange juice in second drink) = (orange juice in final drink)

0.2x + (0.75 - 0.05x) = 2.85

0.15x + 0.75 = 2.85

0.15x = 2.1

x = 14

 

There should be x = 14 liters of the 20% orange juice in the mixture.