How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 25 % ​antifreeze?

Answer 1

Hello Brianna,

To obtain a solution that is 25% antifreeze, one would need to add 3 gallons of water to 1 gallon of pure antifreeze. This is how I came upon my answer:

Before we began, keep in mind that the expression (amount of antifreeze)/(amount of water and antifreeze) determines the percentage of antifreeze in the solution.

Now, to determine how to get the concentration of antifreeze in the solution:

1. Let x be the amount of water added to the solution.
2. Using the expression show above and substituting the values, we get that
3. (1 gallon of antifreeze)/(1 gallon of antifreeze + x) = 0.25
4. Now we have to solve the above expression.
5. Lets first multiple each side by the denominator of that expression, (1 gallon of antifreeze + x)
6. This yields 1 = 0.25*(1 + x) or 1 = 0.25+0.25x
7. Now we solve for x by subtracting 0.25 from both sides, resulting in 0.75 = 0.25x
8. Divide both sides by 0.25 to get what x equal: 0.75/0.25 = x = 3

Therefore, x = 3 or 3 gallons of water are required to be added to attain a solution of 25% antifreeze.

Answer 2

Let's represent antifreeze with A and water with W.

If we want a solution with 1 gallon of antifreeze and an unknown number of gallons of water to be made up of 25% antifreeze, and therefore 75% water, we are looking at a simple comparison of ratios.

A / W = 0.25/0.75

1/W = 0.25/0.75

Since these are just fractions, as long as we invert both sides of this equation the same way, we can turn these fractions upside-down.

W/1 = 0.75/0.25

Anything over one is just itself, so,

W = 0.75/0.25

If you don't have a calculator to tell you at this point that W = 3, you can think of this division as "How many quarters are in three quarters?" Three.

You need 3 gallons of water to make a solution that is 25% antifreeze if you already have 1 gallon of pure antifreeze.

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Another way to think about this is to remember that 25% = 1/4, then realize that if you make our 1 gallon of antifreeze that 1/4 of the solution, then the solution must be made up of 4 gallons total.

Therefore, the other 3/4 of the solution must be made up of 3 gallons of water.