Subject: mixture word problems
Name: Lynne Rae
Who are you: Teacher

How many kg of 30% salt solution by mass and 40% salt solution by mass should be mixed to form 200kg of 37% salt solution by mass?

Hi,

The final mixture is to be 200kg od 37% salt solution by mass. Thus 37% of the 200 kg is salt. 37% of 200 is

 ³⁷/₁₀₀ 200 = 74 kg.

This is made up of some salt from the 30% solution and some from the 40% solution. Suppose that you use x kg of the 30% solution and the remainder, 200 - x kg, from the 40% solution. 30% of the x km from the 30% solution is salt, so the amount of salt contributed to the final mixture from the 30% solution is

 ³⁰/₁₀₀ x kg.

40% of the 200 - x km from the 40% solution is salt, so the amount of salt contributed to the final mixture from the 40% solution is

⁴⁰/₁₀₀ (200 - x) kg.

The sum of these two is 74 kg.

Penny