# Word Problem Question

1. Oct 11, 2006

### DethRose

Ive got an assignment of word problems and cant seem to figure this one out:

A 6 Litre car radiator is 2 thirds full of water. How much of a 90% antifreeze solution (90% is alcohol by volume) must be added to it to make a 10% antifreeze solution in the radiator?

I came up with the equation: 0.9x=(0.1)(6)

but that didnt work so any help about what the way to set up the problem would be great.

2. Oct 11, 2006

### Office_Shredder

Staff Emeritus
How much water is in the radiator?

3. Oct 11, 2006

### DethRose

4L of water

4. Oct 11, 2006

### DethRose

i tried to do it a new way which was :

4+0.9x=(0.1)(6)

but i got a negative number from that attempt so that cant be the answer

5. Oct 11, 2006

### HallsofIvy

Staff Emeritus
You are assuming that the total liquid volume in the radiator is 6 litres. If that were the case, that would mean that you were adding 2 litres of antifreeze solution. But then you would be adding .9(2)= 1.8 litres of pure antifreeze which would give a concentration of 1.8/6.0= 0.3 or 30%. That's too high so you must not be filling the radiator.

Let x be the number of litres of 90% solution you are adding. Then the total liquid volume in the radiator is 4+ x litres. The amount of pure anti-freeze you are adding is (as you say) .9x. The concentration of pure anti-freeze in the radiator is $\frac{.9x}{4+ x}= .1$. Solve that for x.