# Ratio problem

1. Jul 12, 2007

### lLovePhysics

In an 8-gram solution of water and alcohol, the ratio by mass of water to alcohol is 3 to 1. If 12 grams of a solution consisting of 2 grams water for each gram of alcohol is added to the 8-gram solution, what fraction by mass of the new solution is alcohol?

-- I know that the first thing you should do is try to find the mass of alcohol in both the 8-gram and the 12-gram solution. However, to find the amount of alcohol in the 8-gram solution why would you multiply it by 1/4 and not 1/3? Its just confusing how the ratios can be written like 1:3 and then 1/4?

2. Jul 12, 2007

### bel

The mass of the alcohol to water is 1:3, but the mass of the alcohol to the original 8 grammes solution is 1:4, hence multiply by 1/(3+1), hope this clears up the confusion.

3. Jul 12, 2007

### lLovePhysics

Lol, I still don't get it. I know that for every 1 gram of alcohol there are 3 grams of water. I can solve it by doing it that way. But I can't seem to get why it changes when you find the amount of alcohol in the 8-gram solution. Mabye I'm dumb or something. I just suck at ratios.

4. Jul 13, 2007

### HallsofIvy

Do you understand the difference between

"The ratio of alchohol to water is 1:3" and
"The ratio of alchohol to solution is 1:4"?

5. Jul 14, 2007

### lLovePhysics

Well kind of. Solution would be the water + alcohol right? So you just add the msas of alcohol and the mass of water to get 4. Am I doing it correct?

6. Jul 14, 2007

### uart

Yes. Why don't you imagine a really simple example. Say you added one gram of alcohol to 3 grams of water. You now have a total of 4 grams solution of which one gram is alcohol. It's not exactly rocket science as they say. :)

7. Jul 14, 2007

### lLovePhysics

I see! Thanks!