Question

A chemist needs to create a 25% citrus mixture by adding 20 mL of a 80% citrus solution to a 5% citrus solution. How much of each is needed?

Answer 1

You would have to use 55 mL of 5 % citrus solution, and we would get 75 mL of 25 % citrus solution.

Explanation:

80 % citrus means `"80 mL citrus"/"100 mL solution"`

So in 20 mL of 80 % citrus:

`"Volume of citrus" = 20 color(red)(cancel(color(black)("mL soln"))) × "80 mL citrus"/(100 color(red)(cancel(color(black)("mL soln")))) = "16 mL citrus"`

In `x " mL"` of 5 % citrus,

`"Volume of citrus" = x color(red)(cancel(color(black)("mL soln"))) × "5 mL citrus"/(100 color(red)(cancel(color(black)("mL soln")))) = x/20 " mL citrus"`

We add `x " mL"` of 5 % citrus to `"20 mL"` of 80 % citrus to get `20+x " mL"` of 25 % citrus.

`"Total volume of citrus" = (16 + x/20) " mL"`

`"Total volume of solution" = (20+x) " mL"`.

`(16+x/20)/(20+x) = 25/100`

`100(16+x/20)= 25(20+x)`

`1600+5x=500+25x`

`20x = 1600-500 =1100`

`x = 1100/20`

`x = 55`

We have to add 55 mL of 5 % citrus to 20 mL of 80 % citrus and get 75 mL of 25 % citrus.

Check:

`(16+55/20)/(20+55) = 25/100`

`((320 +55)/20)/75 = 25/100`

`375/1500 = 25/100`

`1/4=1/4`

It checks!