Question

Two hundred liters of a 75% acid solution is obtained by mixing a 90% solution with a 50% solution. How many liters of each?

Answer 1

There would be 125 liters of 90% solution and 75 liters of 50% solution.

Explanation:

Let x represent 90% of solution and y represent 50% of solution.

We have been given that there is 200 liters of the solution. We can represent this information in an equation as:

`x+y=200...(1)`

We are also told that two hundred liters of a 75% acid solution is obtained by mixing a 90% solution with a 50% solution. We can represent this information in an equation as:

`0.90x+0.50y=200(0.75)...(2)`

From equation (1), we will get:

`y=200-x`

Upon substituting this value in equation (2), we will get:

`0.90x+0.50(200-x)=200(0.75)`

Let us solve for x.

`0.90x+100-0.50x=150`

`0.40x+100=150`

`0.40x+100-100=150-100`

`0.40x=50`

`(0.40x)/(0.40)=(50)/(0.40)`

`x=125`

Therefore, there would be 125 liters of 90% solution.

Upon substituting
`x=125` in equation (1), we will get:

`125+y=200`

`125-125+y=200-125`

`y=75`

Therefore, there would be 55 liters of 50% solution.