linear equation

Question

one canned juice drink is 30% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 20L that is 22% orange juice?

 

how many liters of the 30% orange just should be in the mixture?

Answer 1

Hi Makayla,

 

Here is how the problem is worked out:

 

0.3x + 0.1y = 0.22*20     (x and y are the volumes in each drink to be added, for a total volume of 20 liters)

 

0.3x + 0.1(20-x) = 0.22*20   (x + y = 20 --> y = 20 - x)

 

 

Simplify the math and solve for one variable first:

0.3x + 2 -0.1x = 4.4

0.2x + 2 = 4.4

0.2x = 2.4

x = 12 liters (this is the volume for the 30% drink)

 

Find the other volume by plugging in x:

y = 20 - x --> y = 20 - 12 = 8 liters (of 10% drink)

 

So the answer is:

12 liters of 30% and 8 liters of 10% drink.

 

Best of luck!