Question

You need 845 mL of a 75% alcohol solution. On hand, you have a 35% alcohol mixture. How much of the 35% alcohol mixture and pure alcohol will you need to obtain the desired solution?

You will need
___ mL of the 35% solution
and
____ mL of pure alcohol.

Answer 1

Let
`x` be the amount (mL) of the 35% solution you need to use, and
`y` the amount (mL) of pure alcohol. Mixed together, you want to end up with 845 mL of solution, so that

`x+y=845`

For each mL of the 35% solution used, there is a contribution of 0.35 mL of alcohol, while each mL of the pure alcohol solution contributes 1 mL of alcohol. You want to end up with a solution at 75% concentration, so that

`0.35x+y=0.75(x+y)=633.75`

We can solve easily by substitution:

`x+y=845\implies y=845-x`

Then

`0.35x+(845-x)=633.75`

`845-0.65x=633.75`

`211.25=0.65x`

`x=325\implies y=520`

So you will need 325 mL of the 35% solution and 520 mL of pure alcohol.