Adding water to paint

Question

A paint company mixes paint with water to create more paint per gallon. They have 10-gallon jugs which contain 10% water. How much water must they add to create a 80/20 mix of paint to water?

 

Please show the steps so I can work it on my own next time. Thank you!

Answer 1

Each jug is 9 gallons of paint and 1 gallon of water. That's 90% paint and 10% water.

 

90% = 0.9,  80% = 0.8,  10% = 0.1, 20%  = 0.2

 

X is the number of gallons of water that is added.

 

So there will be X + 10 gallons.

 

The amount of paint is then:

 

  0.9(10) +  0(X) = 0.8(X+10)   <----   90% paint in the original mixture is added to X gallons of 100% water with no

                                                              paint; the result is (X+10) gallons containing 80% paint

 

9 = 0.8(X + 10)

 

90 = 8(X+10)   <--- multiplies both sides by 10 to clear away the decimals

 

90 = 8x + 80  <--- distributive

 

10 = 8x <--- solves for x

 

10/8 = x

 

x = 5/4  <---- 5/4 gallons of water = 1 and 1/4 gallons = 1.25 gallons

 

 

CHECK:    

 

   The total is 10 + 1.25 = 11.25 gallons which contain 9 gallons of paint. 9/11.25 = 0.8 = 80%