# Homework Help: Algebra- find solution using two variables

1. Dec 15, 2012

### puma072806

1. The problem statement, all variables and given/known data
A chemist ran out of a 72 ml solution of 12% alcohol. All that is left in the lab is 8% alcohol and 20% alcohol. How many ml of 8% and 20% would be needed to make a 72 ml solution of 12%?

2. Relevant equations

3. The attempt at a solution
8x + 20y = 12

2. Dec 15, 2012

### HallsofIvy

What would x+ y represent in this situation?

Of course, if you have x ml of 8% solution then .08x (not "8x") would be the amount of alcohol in it and if you have y ml of 20% solution then .20y would be the amount of alcohol in that. So .08x+ .20y would be the amount of alcohol in the combined soltion. But that is NOT 12 or .12. .12 is the percentage of alcohol in the 72 ml solution. What do you need to multiply the .12 by to get the amount of alcohol? You can then multiply the entire equation by 100 to get rid of the decmals.

3. Dec 15, 2012

### puma072806

Would I multiply .12 by 72 ? Which would then be 8.64

This is what I have so far.

.12 X 72=8.64

.08x + .2y=8.64

(100) .08x + .2y=8.64 (100)

8x + 20y= 864

Last edited: Dec 15, 2012
4. Dec 15, 2012

### kastelian

8x+20y=864 that is good for amount of alcohol
but you are missing one more equation, what's the total amount of liquid that should be made ?

5. Dec 16, 2012

### Ray Vickson

One way to think about such problems is to realize that the figures 12%, 8% and 20% are, essentially, measures of the number of alcohol molecules in a ml of solution. (The actual numbers could be found by going to physical/chemical tables and computing some conversion factors.) When you take a bottle of V1 ml of 8% solution (containing N1 alcohol molecules) and V2 ml of 20% solution (containing N2 alcohol molecules), how much solution do you have altogether? How many alcohol molecules are in the new solution? How does that translate into percentage terms?

6. Dec 16, 2012

### symbolipoint

The big hint is, again, what does x+y represent? What exactly does this example chemist want? Your original equation was good, but you need one more equation.

What HallsofIvy is trying to explain is that you can use decimal fractions instead of percentage, so your first equation can be
0.08x+0.20y=0.12

Last edited: Dec 16, 2012