SOLVING PERCENTAGE PROBLEM
Learning Objective(s)
Identify the amount, the base, and the percent in a percent problem.
Find the unknown in a percent problem.
Introduction
Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they
always have the same denominator, 100. A store may have a 10% off sale. The amount saved
is always the same portion or fraction of the price, but a higher price means more money is
taken off. Interest rates on a saving account work in the same way. The more money you put in
your account, the more money you get in interest. It’s helpful to understand how these percents
are calculated.
Parts of a Percent Problem
Jhonrey has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants
to buy a used guitar that has a price tag of $220 on it. Jhonrey wonders how much money the
coupon will take off the original $220 price.
Problems involving percents have any three quantities to work with: the percent, the amount,
and the base.
The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the
percent off the purchase price.
The base is the whole amount. In the problem above, the whole price of the guitar is $220,
which is the base.
The amount is the number that relates to the percent. It is always part of the whole. In the
problem above, the amount is unknown. Since the percent is the percent off, the amount will be
the amount off of the price.
You will return to this problem a bit later. The following examples show how to identify the three
parts, the percent, the base, and the amount.
Example
Problem Identify the percent, amount, and base in this
problem.
30 is 20% of what number?
Percent: The percent is the number with the %
symbol: 20%.
Base: The base is the whole amount, which in this case is unknown.
Amount: The amount based on the percent is 30.
, Answer Percent = 20%
Amount = 30
Base = unknown
The previous problem states that 30 is a portion of another number. That means 30 is the amount.
Note that this problem could be rewritten: 20% of what number is 30?
Solving with Equations
Percent problems can be solved by writing equations. An equation uses an equal sign (= ) to
show that two mathematical expressions have the same value.
Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of
another amount, you multiply.
The percent of the base is the amount.
Percent of the Base is the Amount.
Percent Base = Amount
In the examples below, the unknown is represented by the letter n. The unknown can be
represented by any letter or a box or even a question mark.
Example
Problem Write an equation that represents the following problem.
30 is 20% of what number?
20% of what number is 30? Rewrite the problem in the form
“percent of base is amount.”
Percent is: 20% Identify the percent, the base,
Base is: unknown and the amount.
Amount is: 30
Percent Base = Amount Write the percent equation.
20% n = 30 using n for the base, which is
the unknown value.
Answer 20% n = 30.
Once you have an equation, you can solve it and find the unknown value. To do this, think about
the relationship between multiplication and division. Look at the pairs of multiplication and
division facts below, and look for a pattern in each row.
Multiplication Division
23=6 6÷2=3
Learning Objective(s)
Identify the amount, the base, and the percent in a percent problem.
Find the unknown in a percent problem.
Introduction
Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they
always have the same denominator, 100. A store may have a 10% off sale. The amount saved
is always the same portion or fraction of the price, but a higher price means more money is
taken off. Interest rates on a saving account work in the same way. The more money you put in
your account, the more money you get in interest. It’s helpful to understand how these percents
are calculated.
Parts of a Percent Problem
Jhonrey has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants
to buy a used guitar that has a price tag of $220 on it. Jhonrey wonders how much money the
coupon will take off the original $220 price.
Problems involving percents have any three quantities to work with: the percent, the amount,
and the base.
The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the
percent off the purchase price.
The base is the whole amount. In the problem above, the whole price of the guitar is $220,
which is the base.
The amount is the number that relates to the percent. It is always part of the whole. In the
problem above, the amount is unknown. Since the percent is the percent off, the amount will be
the amount off of the price.
You will return to this problem a bit later. The following examples show how to identify the three
parts, the percent, the base, and the amount.
Example
Problem Identify the percent, amount, and base in this
problem.
30 is 20% of what number?
Percent: The percent is the number with the %
symbol: 20%.
Base: The base is the whole amount, which in this case is unknown.
Amount: The amount based on the percent is 30.
, Answer Percent = 20%
Amount = 30
Base = unknown
The previous problem states that 30 is a portion of another number. That means 30 is the amount.
Note that this problem could be rewritten: 20% of what number is 30?
Solving with Equations
Percent problems can be solved by writing equations. An equation uses an equal sign (= ) to
show that two mathematical expressions have the same value.
Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of
another amount, you multiply.
The percent of the base is the amount.
Percent of the Base is the Amount.
Percent Base = Amount
In the examples below, the unknown is represented by the letter n. The unknown can be
represented by any letter or a box or even a question mark.
Example
Problem Write an equation that represents the following problem.
30 is 20% of what number?
20% of what number is 30? Rewrite the problem in the form
“percent of base is amount.”
Percent is: 20% Identify the percent, the base,
Base is: unknown and the amount.
Amount is: 30
Percent Base = Amount Write the percent equation.
20% n = 30 using n for the base, which is
the unknown value.
Answer 20% n = 30.
Once you have an equation, you can solve it and find the unknown value. To do this, think about
the relationship between multiplication and division. Look at the pairs of multiplication and
division facts below, and look for a pattern in each row.
Multiplication Division
23=6 6÷2=3
