# Thread: Mixing Water & Antifreeze

1. ## Mixing Water & Antifreeze

How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 60 percent antifreeze?

I understand this to be a mixture problem.
The word PURE tells me that 100 percent somehow applies here.

Here is my attempt. Like always, I seek to know if my equation set up is right or not.

Let w = water that should be added

w + 100 percent (1 gallon) = 0.60(w + 1 gallon)

2. ## Re: Mixing Water & Antifreeze

The equation you have is "w + 100 percent (1 gallon) = 0.60(w + 1 gallon)". I presume you know that "100 percent (1 gallon)" is 1 gallon so that your equation is "w+ 1= 0.60(w+ 1)". That's impossible! If you divide both sides by w+ 1 you get 1= 0.60 which is not true.

Originally you had 1 gallon of liquid anti-freeze. If you add w gallons of water you will have w+ 1 gallons of liquid that is still 1 gallon of anti-freeze. The concentration is 1/(x+ 1)= 0.60.

3. ## Re: Mixing Water & Antifreeze

1/(x+ 1)= 0.60

1 = 0.60(x + 1)

1 = 0.60x + 0.60

1 - 0.60 = 0.60x

0.40 = 0.60x

0.40/0.60 = x

0.6666666667 = x

0.67 = x

Correct?

4. ## Re: Mixing Water & Antifreeze

w = water

1 @100
w @ 0
------------
1+w @ 60

1*100 / (1+w) = 60

Solve: w = 2/3

5. ## Re: Mixing Water & Antifreeze Originally Posted by DenisB w = water

1 @100
w @ 0
------------
1+w @ 60

1*100 / (1+w) = 60

Solve: w = 2/3
I plan to use the MHF to help me with word problems. Not to say that I will not post equations, trigonometry, geometry, etc from time to time. However, I need to target my weakness, DenisB.

It is very frustrating, to say the least, for me to continue struggling with word problems after so many years of answering textbook questions. My goal is to "master" word problems by learning, beyond the shadow of doubt, how to create the needed equation leading to the right answer.

I will post more word problems than anything else here. I will always show my effort and equation set up. I want you and others to correct my work and show me what I did wrong. I will post every word problem that I come across in my textbooks, even and odd number questions.