Algebra word problem

Question

To get 20 liters of a 9% NaCl solution, we mix appropriate amounts of an 8% solution and a 12% solution. How many liters of each do we need?

Answer 1

Let's assign variables  each of these solutions

 

8% solution be x &

 

12% solution be y

 

Now we need to come up with a set of linear equations

 

0.08x + 0.12y = 20(0.09)

 

x + y = 20

 

the first equation  depends  on conc.  the second one on the volume of the mixture we at combining the two solutions.

 

Now I'm going to solve using substitution

 

y = 20 - x

 

plug into the first equation which gives you

 

.08x + .12(20 - X) = 1.8

 

.08x + 2.40 - 0.12x = 1.8

 

- 0.04x = - 0.60

 

x = 15

 

y= 5

 

We are going to use 15 litres of the 8 % soltn. & 5 liters of the 12 % one.

 

Hope  was helpful.