Question

How many kilograms of a 5% salt solution and how many kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution?

Answer 1

31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Explanation:

Let us assume that the number of kilograms of a 5% salt solution used be x .

Let us assume that the number of kilograms of a 15% salt solution used be y .

As given

A 5% salt solution and 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Equation becomes

x + y = 45

5% is written in the decimal form .

`= (5)/(100)`

= 0.05

15% is written in the decimal form .

`= (15)/(100)`

= 0.15

8% is written in the decimal form .

`= (8)/(100)`

= 0.08

Thus

Concentration of 5% salt solution × Number of kilograms of 5% salt solution used + Concentration of 15% salt solution × Number of kilograms of 15% solution used = Concentration of 8% salt solution × Number of kilograms of 8% salt solution

Thus

0.05x + 0.15y = 0.08 × 45

Simplify the above

`(5x)/(100) + (15y)/(100) = (8* 45)/(100)`

5x + 15y = 360

Thus two equations becomes

x + y = 45

5x + 15y = 360

Multiply x + y = 45 by 5 and subtracted from 5x + 15y = 360 .

5x - 5x + 15y - 5y = 360 - 225

10y = 135

`y = (135)/(10)`

y = 13.5 kilograms

Put value of y in the equation

x + 13.5 = 45

x = 45 - 13.5

x = 31.5 kilograms

Therefore the 31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .