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