One canned juice drink is 30% orange juice; another is 10% orange juice. How many liters should be mixed together in order to get 20L that is 21% orange juice?

Question

One canned juice drink is 30% orange juice; another is 10% orange juice. How many liters should be mixed together in order to get 20L that is 21% orange juice?

Answer 1

Here is another way, using simultaneous linear equations.

 

20 Liters has 21% OJ, so that is 4.2 L of pure OJ.

 

So 0.3x + 0.1y = 4.2 expresses the amount of each dilute mixture needed to provide the 4.2 pure OJ.

 

We know x + y = 20.

 

Solve the two equations and you get x = 11 and y = 9.

 

 

Answer 2

if the question said 20%, then it would be half from 30% and half from 10%.

 

But it says 21% which is a little bit closer to 30%. So we will need a little more than 10 liters from 30% and a little less than 10 liters from 10%.

 

So here is one way to do this problem.

 

30% - 21% = 9% difference

 

21% - 10% = 11% difference

 

You add the differences together 9% + 11% = 20%

 

So the final drink is 9/20 from 10% juice and 11/20 from 30% juice.

 

we want 20 liters all together.

 

So we need 11 liters of 30% and 9 liters of 10%