mixture shortcut

analyst218 wrote:if 5% density and 9% density is mixed to create 6% density,
what is the ratio of 5%to9% ?

I have usually solved these types of Q's by
seeing the mixture as a multiple of 6 and find x and y where
5x+9y = multiple of 6
x=3 y =1

but
i just found out there is a short cut where you can
find the ratio for 5% by taking absolute value of 6-9 = 3
find raiot for 9% by taking 6-5=1

ratio 5%to9% = 3:1

will anyone explain why this is possible?

if you take X units of 5% liquid and Y units of 9% liquid, you get a 6% mixture.

In other words :

5X+9Y = 6(X +Y)

or X=3Y

or the ratio in which the two are mixed (X/Y) is 3:1.

analyst218 wrote:if 5% density and 9% density is mixed to create 6% density,
what is the ratio of 5%to9% ?

We can plot the densities on a number line:

Group A ----- x------- Average --------------- y ------------------ Group B

x and y represent how far group A and group B, respectively, are from the average.

The ratio of Group A to Group B will always be the same as the ratio of y to x, or in other words:

A:B = y:x


5% ---- 1----- 6% -------------3--------------9%

In this case, x=1% and y=3%, so:

3%/1% = 3/1

Therefore, the ratio of the 5% to the 9% is 3 to 1.