A car radiator has a 6-liter capacity. If the liquid in the radiators 40% antifreeze, how much liquid must be replaced with pure anitfreeze to bring the mixture up to a 50% solutions? If I told you the answer is 1 liter, in your own words, using complete sentences explain how you would solve this problem

Question

A car radiator has a 6-liter capacity. If the liquid in the radiators 40% antifreeze, how much liquid must be replaced with pure anitfreeze to bring the mixture up to a 50% solutions? If I told you the answer is 1 liter, in your own words, using complete sentences explain how you would solve this problem

Answer 1

To solve this problem, we need to calculate the amount of liquid that needs to be replaced with pure antifreeze. We know that the radiator has a 6-liter capacity and the current mixture is 40% antifreeze. We want to bring the mixture up to a 50% solution.

To start, we can calculate the amount of antifreeze currently in the radiator. Since the radiator has a 6-liter capacity and the mixture is 40% antifreeze, we can multiply the capacity (6 liters) by the concentration of antifreeze (40%) to find the current amount of antifreeze in the radiator.

So, (6 liters) x (40%) = 2.4 liters of antifreeze.

Next, we need to determine the desired concentration of antifreeze to get a 50% solution. Since we want to bring the mixture up to a 50% concentration, we subtract the current antifreeze amount (2.4 liters) from the amount needed for a 50% solution (which is unknown) to find the additional antifreeze we need.

Let's call the unknown amount of antifreeze we need "x". So, (x liters) - (2.4 liters) = the additional antifreeze needed.

Now, since the desired concentration is 50%, the remaining liquid in the radiator after replacing some of it with pure antifreeze will be 50% antifreeze. This means that the remaining liquid should be equal to the amount of antifreeze already in the radiator (2.4 liters).

So, (6 liters - x liters) x (50%) = 2.4 liters.

We can now solve for "x" by rearranging the equation:

(6 - x) x 0.5 = 2.4

Dividing both sides by 0.5:

6 - x = 4.8

Finally, we can solve for "x" by subtracting 6 from both sides of the equation:

-x = 4.8 - 6
-x = -1.2

To isolate "x", we multiply both sides by -1:

x = 1.2

So, the amount of liquid that needs to be replaced with pure antifreeze to bring the mixture up to a 50% solution is 1.2 liters. Since we typically deal with whole numbers, we can round this to 1 liter, which matches the given answer.