Lisa will make punch that is 25% fruit juice by adding pure fruit juice to a 2-liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add?

Mar 25, 2015

Let's call the amount to be found $x$

Then you will end up with $x + 2$ L of 25% juice

This will contain $0.25 \left(x + 2\right) = 0.25 x + 0.5$ pure juice.

The original 2 L allready contained $0.10 \cdot 2 = 0.2$ juice

So we added $0.25 x + 0.3$ juice
But this is also $x$ (as x=100% juice)

$\to 0.25 x + 0.3 = x \to 0.75 x = 0.3 \to x = 0.4$ liter.

Mar 25, 2015

I think $0.4 l$.

Have a look if it makes sense:

Mar 25, 2015

Suppose Lisa adds $k$ liters of pure juice

The total amount of punch will be:
$2 + k$
and the amount of pure juice in this is to be
25% xx (2+k) liters

The original punch contains
10% xx 2 liters of pure juice
which when combined with
$k$ liters at 100% will give a total of (10% xx 2) + (100% xx k)# liters of pure juice.

So,
$\left(10 \times 2\right) + \left(100 \times k\right) = 25 \times \left(2 + k\right)$
which simplifies to
$20 + 100 k = 50 + 25 k$
$75 k = 30$
$75 k = 30$
or
$k = \frac{2}{5} = 0.4$ liters