Mixing Ratio Formula

Question

Mixing Ratio problem

I need to blend two different hardnesses of rubber together to get a certain hardness.
One is 40 hard the other 60 Hard

Example
40 60 blended in 1:1 ratio is equal 50 hard

40 60 blended in 1:3 ratio is equal 55 hard. [(1x40)+(3x60)]/4 = 55

How do i find the ratio needed if for instance i needed 58 hardness?

Answer 1

There is method called alligation.  This is where you put what you have on the left of a tic-tac-toe grid, what you want in the middle, and what you use on the right side. Then you subtract the values cross-wise (diagonally) to get what you need. An example for 58 hardness is shown below.

HAVE..........WANT.......NEED

40...............................2....

..................58...................

60..............................18...

This shows that you need to use 2 parts of the 40% and 18 parts of the 60%.  The parts can be anything (ounces, grams, etc).  This will result in 20 parts total.  So, if you want to make 100 parts, you just multiply by 5 and use 10 parts of 40% and 90 parts of 60%.

 

If you want to use algebra to solve this problem, and say you want 100 parts, then ...

(x parts)(40%) + (100-x parts)(60%) = 100 parts x 58%

40x + 6000 - 60x = 5800

20x = 200

x = 10 parts of 40% and 90 parts of 60%