Solving Word Problem: Fill 6L Car Radiator w/ 10% Antifreeze Solution

[DethRose]

Ive got an assignment of word problems and can't 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.

 

[Office_Shredder]

First, this should probably be in the homework section, but oh well

Second, you hvae to ask yourself a different question (which you don't seem to have taken into account)

How much water is in the radiator?

 

[DethRose]

4L of water

 

[Office_Shredder]

Ok, this whole posting in two places isn't going to cut it, so I'm just going to stick with this thread.

If the anti-freeze solution is 90% antifreeze, then when you add a volume V of solution to a volume v of liquid, your total volume becomes V + v, and your anti-freeze portion is .9V. So how can this be applied to the problem?

 

[DethRose]

ah

so the equation should be 4+.9V=6(.1)?

 

[DethRose]

is that correct?

 

[DethRose]

ok i tried that equation and got an answer of -3.77777 so that can't be the correct answer, so i am kind of stumped as to what to try next lol.

 

[Office_Shredder]

You have to explain WHY you think that's the equation. I don't know why you think there should be a 6 at all, for example, so it's difficult to help you

 

[HallsofIvy]

You seem to be thinking that the radiator must be filled. That's obviously incorrect- in order to fill the radiator, you would have to add 2 litres of 90% antifreeze which would NOT give you a 10% solution.

Let x be the number of litres of antifreeze added. Then you have 4+ x litres of liquid in the radiator. Since the antifreeze solution is 90% anti-freeze, you have added 0.9x litres of antifreeze. For that to be 10% of the entire amount, you must have 0.9x= 0.1(4+ x). Solve that equation for x.