Question

One canned juice drink is 15% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 10 L that is 14% orange juice?

Answer 1

`9` liters of 15% orange juice and `1` liter of 5 % orange juice.

Explanation:

Let `x` be the number of liters of `15%` juice, and
`y` be the number of liters of `5%` juice.

Then `x + y = 10`

and `0.15x + 0.05y = 1.4`

(there are `1.4` liters of orange juice in a 14% solution of 10 liters--made up of `0.15x` liters of `15%`, and `0.05y` of `5%`)

These equations can be easily solved.

Divide the second by `.05" "rarr: 3x + y = 28`
Then subtract the first equation:

`(3x + y) - (x + y) = 28 - 10`
`3x +y -x -y = 18`

which simplifies to `2x = 18`

So `x =9`

And since `x + y = 10`, we get `y = 1`