Finding a Number Given Percentage of Whole

On some percentage problems, you may be asked to find the whole given a part and a percentage. For instance, on this example here we’re asked to find the whole number that 30 is x percent of for each of these values of x.

To do this, we need to figure out what equation to use. We’ll use A to represent the number we’re looking for. We can say that A times x percent is equal to 30. We can simplify this by dividing both sides by x.

The x’s on this side cancel, and that leaves us with A equals 30/x%. That’s the formula we’ll be using to find A for each of these values of x. For x equals 20%, we can say that A equals 30/20%. It’s going to be easiest to work with fractions in this case.

The fractional equivalent of 20% is 1/5. We can say that A equals 30 over 1/5, or 30 times 5/1. If we multiply this out, what we find is that A equals 150. 30 is 20% of 150. In the next example, we have the value of x as 40%.

We can write A equals 30/40%. Once again, we’re going to convert this to a fraction. 40% is the same as 2/5, so A is equal to 30 over 2/5, or 30 times 5/2. Now, we can cancel here, dividing 30 and 2. We get 5 and 1. 15 and 1.

We can multiply this out. 15 times 5 is 75. 30 is 40% of 75. In the final example, we have 75%. We can write that A equals 30 over 75%. The fractional equivalent of 75% is 3/4, so we can write that A equals 30 over 3/4, or 30 times 4/3. Once again, we can cancel. We’ll divide 30 by 3 to get 10 and 3 by 3 to get 1. All we’re left with here is 10 times 4, which is 40. 30 is 75% of 40.