A car radiator needs a 40​% antifreeze solution. The radiator now holds 18 liters of a 10​% solution. How many liters of this should be drained and replaced with​ 100% antifreeze to get the desired​ strength?

Answer 1

Let's start by finding the amount of antifreeze currently in the radiator.
At present, the radiator holds 18 liters of a 10% antifreeze solution, so the amount of antifreeze in the radiator is 18 liters * 10% = 1.8 liters.

Now, let's determine how much antifreeze needs to be in the radiator for a 40% concentration.
If we let x represent the amount of the 10% solution to be drained, then we can set up the equation:
(1.8 liters + x) = 0.4 * (18 liters - x)

Expanding this equation, we get:
1.8 liters + x = 7.2 liters - 0.4x

Combining like terms, we have:
1.8 liters + 0.4x = 7.2 liters - x

Now, let's solve for x:
1.4x = 5.4 liters

Dividing both sides by 1.4, we find:
x = 3.857 liters

Therefore, approximately 3.857 liters of the 10% solution should be drained and replaced with 100% antifreeze to get the desired 40% strength.