Division and Unit of measurement change

Question

I have a 2 gal container that must be filled with bleach and water. I need to mix water and bleach at a 10-1 ratio. 10 parts water, 1 part bleach.

How many quarts of bleach will I use in the mix?

Answer 1

Use a ratio to find the proportions. Let W = amount of water

B = amount of bleach

Then,

(10 gallons W)/(1 gallon B) = (x gallons W)/(2-x gallons B)

(2-x)10 = x or 20 - 10x = x or 11x = 20

Then,

x = 20/11 gallons of water and (2 - x) = 2 - 20/11 = 2/11 gallons of bleach