Panchito has two solutions available in the lab, one with 5% alcohol and another with 13% alcohol. How much of each should he mix together to obtain 6 gallons of a solution that contains 8% alcohol?

Answer 1

let x be the amount of 5% alcohol solution

then 6-x is the amount of 13% alcohol solution

set up an equation

.05x + .13(6-x) = .08(6)

solve for x

then find 6-x

Answer 2

Answer 3

Hadi's answer is textbook perfect, and the popular answer, but I recorded a video, and I hope it works.

It doesn't look like it did.

You have a seesaw with 5% on one end and 13% on the other. The balance point is at 8%.

5% is 3 away from 8% which is 5 away from 13%. In order for the seesaw to be balanced, you need

5 parts of 5% solution for every 3 parts of 13% solution. (the farther you are from the balance point, the more leverage you have).

There are 8 parts in total. 8 parts = 6 gallons, so 1 part is .75 gallons.

5 parts of 5% solution = 5 * .75 = 3.75 gallons.

3 parts of 13% solution = 3 * .75 = 2.25 gallons.

3.75 + 2.25 = 6 gallons, just to make sure.