7.3 Notes - Solve Basic Percent Problems
Warm-up: Distance
This map shows the approximate location of some of the U.S. state capitals. In the
map, 1 inch represents 656 miles.
1) On this map, the distance between Denver, Colorado and Tallahassee, Florida, is
approximately 2 inches. Write and solve a proportion to find the distance between these
two capitals.
2) On this map, the distance between Tallahassee, Florida, and Madison, Wisconsin,
is approximately 1
7
16
inches. Write and solve a proportion to find the distance between
these two capitals.
3) On this map, the distance between Denver, Colorado, and Carson City, Nevada, is
approximately 1
1
8
inches. Write and solve a proportion to find the actual
distance between these two capitals.
4) In your own words, define percent:
Page
is p

of 100
1
Goal  Solve different types of percent problems.
SOLVING PERCENT PROBLEMS USING PROPORTIONS
You can represent "a is p percent of b " by using the proportion:
a
p
where “a” is the ______________, “b” is the _______________, and “p” is the
=
b 100
______________________________.
Many of the problems can be set into a proportion by thinking of the proportion as:
THREE BASIC TYPES OF PERCENT PROBLEMS:
Example 1 - Find a percent using a proportion (TYPE 1)
What percent of 50 is 33?
Write a proportion where 50 is the base and 33 is part of the base.
a
p

b 100
or

is p

of 100
p
100
Write proportion.
Substitute _____ for a and _____ for b.
Use the cross products property
33 is _________ of 50.
Now You Try It! Use a proportion to answer the question.
1) What percent of 80 is 28?
2) What percent of 90 is 36?
Example 2 - Find a part of a base using a proportion (TYPE 2)
What number is 75% of 64?
Write a proportion where 75 is the percent and 64 is the base.
a
p or

b 100
a
is p

of 100

100
Write proportion.
Substitute _____ for b and _____ for p.
Use the cross products property
____________ is 75% of 64.
Now You Try It! Use a proportion to answer the question.
Page
2
3) What number is 35% of 80?
4) What number is 110% of 75?
Example 3 - Find a base using a proportion (TYPE 3)
21 is 37.5% of what number?
Write a proportion where 37.5 is the percent and 21 is part of the base.
a
p

b 100
is p

of 100
or
b

Write proportion.
Substitute _____ for a and _____ for p.
100
Use the cross products property
21 is 37.5% of ________________.
Now You Try It!
5)
Use a proportion to answer the question.
27 is 25% of what number?
6) 78 is 150% of what number?
What percent of 252 is 84?
Find part of a base.
What number is 30% of 90?
Find a base.
16 is 20% of what number?
3
Find a percent.
Proportion/Equation
Page
SUMMARY: TYPES OF PERCENT PROBLEMS
Percent Problem
Example