Question

How much `90%` saline solution should we mix to `3qt.` of `15%` saline mix to make `45%` saline solution?

Answer 1

`2` `"qt."`

Explanation:

Let `x` and `y` be the number of `"qt."` of the `90%` solution and the number of `"qt."` of `45%` solution, respectively.

We can then express the problem mathematically as:

`Rightarrow x + 3 = y`

`or`

`Rightarrow x` `"qt. of"` `90%` `"solution"` `+ 3` `"qt. of"` `15%` `"solution"` `=` `y` `"qt. of"` `45%` `"solution"`

`Rightarrow x times 0.90 + 3 times 0.15 = y times 0.45`

`Rightarrow 0.90 x + 0.45 = 0.45 y`

`Rightarrow 0.90 x = 0.45 y - 0.45`

Then, let's substitute the first mathematical expression in place of `y`:

`Rightarrow 0.90 x = 0.45 (x + 3) - 0.45`

`Rightarrow 0.90 x = 0.45 x + 1.35 - 0.45`

`Rightarrow 0.45 x = 0.90`

`therefore x = 2`

Therefore, we need to mix `2` `"qt."` of the `90%` saline solution with `3` `"qt."` of `15%` saline solution to make a `45%` solution.

Answer 2

We need `2` qt. of `90%` saline solution.

Explanation:

Let us assume that we need to mix `x` qt. of `90%` saline solution. It will have `x xx90/100=0.9x` qt. saline.

It is mixed with `3`qt. of `15%` saline solution, this as `3xx15/100=0.45` qt. saline

and on mixing the two, the total quantum of saline is `0.9x+0.45` qt.

This is `45%` of `x+3` or `(x+3)xx0.45`

hence `0.45(x+3)=0.9x+0.45`

or `0.45x+1.35=0.9x+0.45`

or `0.9x-0.45x=1.35-0.45`

or `0.45x=0.9`

i.e. `x=0.9/0.45=2`

Hence, we need `2` qt. of `90%` saline solution.