Solve the 6 Litre Car Radiator Word Problem | 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]

How much water is in the radiator?

 

[DethRose]

4L of water

 

[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 can't be the answer

 

[HallsofIvy]

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.