# 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?

Oct 10, 2015

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 $y = m x + c$
takes on the value of 20%

("change in detergent content of mix y-axis")/("change in quantity of material added x-axis") = (100%-20%)/(100%-0%)

Target (y value in equation):
The target % content in the final mix : 24%

The amount of pure detergent to be added to blend: $x$

Putting this together:
$24 = \frac{80}{100} x + 20$

Now it is a simple matter of manipulation to find $x$ and hence the final masses of constituents for a total of 140Kg of product.

I will leave you to work that out.