There are three basic types of percent problems:
1. Finding a given percent of a given number. For example, find 25% of 640.
2. Finding a percent when we’re given 2 numbers. For example, 15 is what percent of 50?
3. Finding a number which is a given percent of some other number. Like: 10 percent of which number is 12?
So let’s start with the first type, finding a given percent of a given number.
1. Finding a Given Percent of a Given Number
Let’s start with our first type of percent word problem.
As an example: What number represents 25 percent of 640?
Here is our Solution:
x represents our unknown number. So we translate our words into a simple equation.
The question is: Which number represents 25 percent of 640, so x = 25% · 640
So we have to solve this equation for x.
Our original equation is x = 25% · 640
If we change 25 percent to a decimal, we get: 25% = 0.25
So: x = 0.25 · 640
When we multiply: 0.25 and 640 we get 160.
So: x = 160 and thus: 25% of 640 = 160.
2. Finding a Percent when We’re Given Two Numbers
Next, let’s take a closer look at the 2nd type of percent problem.
For example, 15 is which percent of 50?
Well, let x represent our unknown percent. Then we can translate these words (15 is which percent of 50) into the following equation”
15 = x · 50
The Math ‘commutative property of multiplication’ lets us change the multiplication order on the equation’s right-hand side.
We’ll get: 15 = 50x. So now, we will be able to solve this equation for x.
The original equation is 15 = 50x.
When we divide both sides of this equation by 50 we get 15/50 = 50x/50.
Now we can simplify the right-hand side of the equation into 15/50 = x
When we divide 15/50, we get 0.30. So x = 0.30
But notice that we have to express the answer as a percent. To get a percent, we’ll simply have to move our decimal 2 places to the right (and, of course, add the percent symbol).
So, 0.30 = 30% and thus, 15 is 30 percent of 50.
3. Finding a Number which is a Given Percent of some other Number
Now, let’s look at the third item on our list of basic types of percent problems that we started this page with.
For example, ten percent (10%) of which number is 12?
For the solution, we say that x represents our unknown number. So we can translate our words into the following equation.
Original question: 10% of which number is 12? So: 10% · x = 12.
When we change 10% into a fraction, we get: 10% = 10/100 = 1/10.
So 1/10x = 12
And now, we’ll be able to solve the equation for x.
When we multiply both sides of the equation by 10 we get:
Simplifying gives us: x = 120. Thus, ten percent (10%) of 120 is 12. So now, you’ve learned all about the three main types of solving percent word problems.