Solving Percentage Problems

There are two easy ways of solving Percentage problems. We will look at translating the word problem into algebraic expressions in this video. This method requires you to just write the word problem mathematically and solve the resulting equation

We will learn how to find the percent of a number. We will also learn what percentage a number is of another number, and finally we will use percentage to find a number

Let’s look at these individually and we will use the idea of proportion to make these even easier.

 

Finding the percentage of a number

Find 60% of 200.

Here we know 60% is 60/100 .

“of” in mathematics means multiplication

So writing this algebraically we will have

  60/100  x 200

From here we just simplify to get 120

so 60% of 200 is 120. Watch video for details

Example 2.

Find 50% of 24.

This will be 50/100 times 24.

Again we know that "of" in mathematics means multiplication

We can solve this to get 12

Therefore 50% of 24 is 12. Watch video for details

 

What percentage of a number is another number?

Let's look at this question. What percent of 10 is 2?

The statement “What percent” is what we are looking for, so let’s represent it by P%.

We know that P% is P/100.

Also we know “of” means multiplication.

“Is” is the same as “is equal to”.

So we have equal to 2.

We will have P/100 x 10 = 2

From here we can just solve for P.

So our answer is 20%. Watch video for details

Please do not get confused when things are twisted. It is the same procedure.

Example 2.

8 is what percentage of 24?

So we know we can write it as

8 = P% x 24.

Again we change the P% to P/100.

"of" means multiplication

"is" means "equal to"

So now we solve for P.

After solving we will have 33.33%

 

Use percent to find a number

Example

5% of what number is 20.

Here again we can just follow the mathematical meaning.

First we know 5% means 5/100.

“of” means multiplication.

“What number” is what we are looking for, so we will represent it by N.

We know “is” means equal to.

Then we have our 20.

So we have 5/100 x N = 20

We can now simply solve for N.

 N = 400. Watch video for details

This brings us to the end of this Lesson. Have a Great Day