Question

A laboratory technician needs to make a 117-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration?

Answer 1

Given

A laboratory technician needs to make a 117-liter batch of a 20% acid solution.

 How much the  technician combine  an acid solution that is pure acid with another that is 10% to get the desired concentration.

To proof

let us assume that the solution that is pure acid = x liters

let us assume that the anthor solution that is 10% = y liters

Than

the  equation becomes

x + y = 117

As given in the question

technician needs to make a 117-liter batch of a 20% acid solution

laboratory technician combine  an acid solution that is pure acid with another that is 10% to get the desired concentration

Convert 20% in the simpler form

$=\frac{20}{100}$

= 0.2

Convert 10% in the simpler form

$=\frac{10}{100}$

= 0.1

Than the equation becomes

0.2 × 117 = x + 0.1y

234 = 10x + y

Than the two equation are  

x + y = 117

234 = 10x + y

subtracted x + y = 117 from 234 = 10x + y

10x+y -x -y = 234 -117

9x = 117

x= 13

put this in the equation x + y = 117

13 + y =117

y = 117 - 13

y = 104

Therefore

The solution that is pure acid be 13 liters.

than the other solution that is 10% is 104 liters.

Hence proved