How many liters of a 8% salt solution must be mixed with 14 liters of a 38% salt solution to obtain a 20% salt solution?

Question

I need help with solving this word problem

Answer 1

A really useful method for these kinds of problems is referred to as "alligation". Look it up for a better explanation than what I can provide here.  You put what you have on the left, what you want in the middle, and then subtract criss-cross wise to get the parts of each.  Something like this...

 

HAVE..........WANT.......PARTS......

8%.............................18

.................20%................

38%............................12

So, you need 18 parts of the 8% and 12 parts of 38%.

Since the 12 parts equals 14 liters, then 18 parts will equal 21 liters.

Answer 2

We mix x liters of 8% salt

We add 14-x liters of 38% salt

 

.08x + .38(14-x) = .2(14)

.08x + 5.32 - .38x  = 2.8

 

Solve for x to find amount of

8% solution.

14-x will be the amount of38% solution.