Systems of equations help.

Question

Solution x is 20% alcohol and solution y is 80% alcohol. How much of each should be used to make 100 / of a 50% solution? 

Answer 1

let x be the amount of solution x and let y be the amount of solution y.

 

After you've done the mixing, you will have a total of 100 l, so you can say x + y = 100

 

Since solution x is 20% alcohol, or .2, that means that the amount of alcohol in solution x is .2x.

 

And similarly, the amount of alcohol in solution y is .8y.

 

So there will be a total amount of alcohol of .2x + .8y

 

Since you want the solution at the end to be 50% alcohol, it will need to have .5 * 100 l of alcohol = 50 l.

 

So .2x + .8y = 50.

 

So you have to solve the following equations together:

 

x + y = 100

.2x + .8y = 50

 

Divide the second equation by .2:

x + 4y = 250

 

Subtract the first equation from this:

x + 4y = 250

x + y = 100

----------------

3y = 150

 

So y = 50.

 

Since x + y = 100, x must also be 50.

 

So you need 50 l of each solution.