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
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(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.

Mar 25, 2015

I think #0.4 l#.

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

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,
#(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