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?

Question

7422 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-18T02:39:33

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

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 $y = 1$