Word Problems with Percentage

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A percent is a comparison of 2 numbers.  By itself, it is not very meaningful.  What does this mean? A percent is not an actual value, it just tells us something about 2 values. You need to know what are the 2 numbers being compared.

Look at this question:

A dress costs $100.  It’s price was decreased by 10% during a sale.  After the sale, the price of the dress was increased by 10%.

When you read that question, you may automatically assume that the price of the dress after the sale is back to $100.  That would not be correct.  Look at the working below.

An easy way to understand this is 10% of $100 and 10% of $50 give two different values, even though both are 10% of something.

When working with percentages, always figure out which 2 numbers are being compared. 

Percentage and Proportion

You can also work with percentages as a proportion.

Look at this example.

I bought some fruits. 20% of them are apples and the remainder are oranges.  How many oranges did I buy if I bought 13 apples?

Some methods to use in solving word problems.

Let’s look at some ways of solving percentage problems.

There are 2 main types of percentage questions.  In the first type, the values are given and you have to find the percentage by comparing the values.

Look at this example.

There are 60 children in the park.  20 are boys.  What percentage of the children  are boys?

The first method is to make use of fractions. 20 boys out of 60 children.

The second method is to work everything out step by step.

We can condense method 2.

The last method is to use proportion.

If you study all the methods carefully, you will realize that they are basically the same way of solving the problem but written in different ways.

Try each method so you have a better understanding of percentages and how to solve word problems.

Second type of percentage questions

The second type of question is where the value of one percentage is given and you have to find the value of a different percentage.

Here is an example.

20% of a number is 60.  What is the number?

The first method is to use fractions.

The second method is a simpler version of method 1.

The next method is a condensed version of method 2.

The last method is by using proportion.

Percentages greater than 100%

Percentages does not always have to be less than 100.  You can add and subtract percentages in the usual way as other numbers.

Look at this example.

George and Mary shared $380.  George’s share of the money is 90% of Mary’s share.  How much is George’s share?

Practice Worksheet

Worksheet 1

Worksheet 1 ANSWER