Question

A chemist has 30% and 60% solutions of acid available. How many liters of each solution should be mixed to obtain 570 liters of 31% acid solution? Work area number of liters | acid strength | Amount of acid 30% acid solution 60% acid solution 31% acid solution liters of 30% acid liters of 60% acid

Answer 1

Let the amount of 30% acid solution be a

Let the amount of 60% acid solution be b

Given, "a" and "b" mixed together gives 570 liters of 31% acid. We can write:

`0.3a+0.6b=0.31(570)`

Also, we know 30% acid and 60% acid amounts to 570 liters, thus:

`a+b=570`

The first equation becomes:

`0.3a+0.6b=176.7`

We can solve the second equation for a:

`\begin{gathered} a+b=570 \\ a=570-b \end{gathered}`

Putting this into the first equation, we can solve for b. The steps are shown below:

`\begin{gathered} 0.3a+0.6b=176.7 \\ 0.3(570-b)+0.6b=176.7 \\ 171-0.3b+0.6b=176.7 \\ 0.3b=176.7-171 \\ 0.3b=5.7 \\ b=(5.7)/(0.3) \\ b=19 \end{gathered}`

So, a will be:

a = 570 - b

a = 570 - 19

a = 551

Thus,

551 Liters of 30% acid solution and 19 Liters of 60% acid solution need to be mixed.