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?

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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?

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Answer 1 · 2015-03-25T12:18:47

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

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

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

The original 2 L allready contained $0.10*2=0.2$ juice

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

$->0.25x+0.3=x->0.75x=0.3->x=0.4$ liter.

Answer 2 · 2015-03-25T12:36:53

I think $0.4 l$ .

Have a look if it makes sense:
enter image source here

Answer 3 · 2015-03-25T12:37:14

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,
$(10 xx 2) + (100 xx k) = 25 xx (2+k)$
which simplifies to
$20 + 100k = 50 + 25k$
$75k = 30$
$75 k = 30$
or
$k = 2/5 = 0.4$ liters

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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?

3 Answers

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