# 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?

Dec 18, 2016

$9$ 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 $0.15 x + 0.05 y = 1.4$

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

These equations can be easily solved.

Divide the second by $.05 \text{ } \rightarrow : 3 x + y = 28$
Then subtract the first equation:

$\left(3 x + y\right) - \left(x + y\right) = 28 - 10$
$3 x + y - x - y = 18$

which simplifies to $2 x = 18$

So $x = 9$

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