how many liters of a 5% alcohol solution should be mixed with 15 liters of a 10% alcohol solution to obtain a mixture that is 8%alcohol

Question

how many liters of a 5% alcohol solution should be mixed with 15 liters of a 10% alcohol solution to obtain a mixture that is 8%alcohol

Answer 1

Let's start with the fact that you know you have 15 liters that is 10% alcohol. That solution has 1.5 liters of alcohol and 13.5 liters of other liquid.

 

You don't know how many liters of 5% alcohol you have, so let's call that L. That means you have .05L liters of alcohol and .95L liters of other liquid.

 

When you combine the 2 mixtures you will have a total of L + 15 liters of alcohol solution.

When you combine the 2 mixtures you will have a total of .05L + 1.5 liters of alcohol.

 

So the total amount of alcohol divided by the total amount of liquid must come out to 8%.

 

(.05L+1.5) / (L + 15) = .08    cross multiply to get...

.05L + 1.5 = .08L + 1.2

L = 10

 

So 10 liters of 5% alcohol will dilute your 15 liters of 10% alcohol to and 8% solution.

 

Hope this helps.