Question

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?

Answer 1

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

I think `0.4 l`.

Have a look if it makes sense:

Answer 3

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