Question

A chemist needs 140 milliliters of a 73% solution and has only 37% and 79% solutions available. How many milliliters of each should be mixed to get the desired solution?

Answer 1

I am going to show you two approaches
Method 1 of 2

120 ml of 79% concentration
`color(white)(1)`20 ml of 37% concentration

Explanation:

There is a direct link in quantities of each the solutions.

If you have `x` of one solution then the other is `140-x`

So if we only consider the strongest solution we are directly inferring the weaker one.

If we have all the stronger solution the concentration is 79%
If we have all the weaker solution (none of the stronger) the solution concentration is 37%

Every other possible blend will be between. So we have the situation of:

The slope of part is the same as the slope of all.

`(79-37)/140 = (73-37)/x`

Turn it all upside down:

`140/(79-37) = x/(73-37)`

`140/42=x/36`

`x=(36xx140)/42= 120`

120 ml of 79% concentration
`color(white)(1)`20 ml of 37% concentration

Answer 2

Method 2 of 2: have a look at method 1 first.

`120 ml` at 79% concentration

`20 ml` at 37% concentration

Explanation:

Let the amount of 79% concentration be `x`
Let the amount of 37% concentration be `(140-x)`

`79%x+37%(140-x)color(white)("ddd")=color(white)("d")73%140`

`(79x)/100color(white)("d")+(37xx140)/100-(37x)/100color(white)("dd")=(73xx140)/100`

Multiply both sides by 100

`79x+5180-37x=10220`

`42x=5040`

`x=120` at 79% concentration

`140-120=20` at 37% concenttration