# How many kilograms each of a powdered detergent and a rinsing solution containing 20% of the pure detergent must be mixed to make 140 kilograms of a 24% rinsing solution?

##### 1 Answer

5% of 140Kg pure detergent 95% of 140Kg rinsing solution

#### Explanation:

This condition may be represented by a strait line graph.

Defining content of only one of the two constituents as a % implies directly how much of the other is used. Together they must add up to 100%.

The question defines the initial conditions. Hence we have the ability to determine the extreme case of zero content ( all the other one) to only that material ( none of the other one ).

In this case

No pure detergent => 20% detergent in final product

Only pure detergent => 100% detergent in final product

The constant (c) in the standard form equation of

takes on the value of 20%

The gradient (m) :

Target (y value in equation):

The target % content in the final mix : 24%

The amount of pure detergent to be added to blend:

Putting this together:

Now it is a simple matter of manipulation to find

I will leave you to work that out.