A car radiator needs a 60% antifreeze solution. The radiator now holds...

Question

A car radiator needs a 60% antifreeze solution. The radiator now holds 40 liters of a 50% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?

Answer 1

The way the problem is written suggest 40 liters is the capacity of the radiator, and we want to fill it. I hope I have that right.

 

So if x is the number of liters you take out, then

 

40 (0.6) = (40 - x)(0.5) + x (1.0)

 

On the left-hand side is what you want. On the right-hand side is what you are taking out plus what you are putting in. The concentration of antifreeze I have converted from percentage to decimal.

 

This comes out to

 

24 = 20 + 0.5x

 

and x = 8 liters. Cheers!