Math 40
Prealgebra
Section 7.3 – General Applications of Percent
7.3 General Applications of Percent
Translating to a Percent Equation
Percent word problems can be translated into the following:
The amount of __________  % of __________ Total
The phrase that goes in the blanks comes from the information given in the word problem. Both
blanks should have the same exact words.
Note: In other books the equation above is also written as
The amount of __________  % of __________ Base
A R B
EX: Sandra takes roll in her class and finds that 104 students are present. If this is 80% of the total
class enrollment, how many students are in the class?
The amount of __________  % of __________ Total
From reading the question we can see that they want us to find the TOTAL number of students in the
class. We are given the amount of students present and the percent of students present. Notice
the underlined phrases are the same. This is what goes in the blanks of our translated percent
equation.
The amount of students present = % of students present
Total
Now let’s solve the example using the Five Step Word Problem Method,
1) Identify a variable.
t  the total number of students
2) Write an equation.
The amount of __________  % of __________ Total
The amount of students present = % of students present
Total
104
0.80
t
104  0.80 t
3) Solve the equation.
104  0.80 t Divide both sides by 0.80 to solve for t
104 0.80t

0.80 0.80
130  t
4) State your answer.
There are 130 students in Sandra’s class.
5) Check your answer.
Does the answer makes sense? Yes!
Did you answer what the problem is asking for? Yes!
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Math 40
Prealgebra
Section 7.3 – General Applications of Percent
Example 1: Myrna notes that 20% of her class is absent. If the class has 45 students, how many students are
absent?
Solution: We need to find the amount of students absent. The percent given is the percent of students absent.
From this we have,
The amount of __________  % of __________ Total
The amount of students absent = % of students absent
Total
1) Identify a variable.
A  the amount of students absent
2) Write an equation.
The amount of __________  % of __________ Total
The amount of students absent = % of students absent Total
A
0.20
45
A  0.20 45
3) Solve the equation.
A  0.20 45
9
A9
4) State your answer.
There were 9 students absent in Myrna’s class.
5) Check your answer.
Does the answer makes sense? Yes!
Did you answer what the problem is asking for? Yes!
You Try It 1: Aaron notes that 15% of his class is absent. If the class has 80 students, how many students are
absent?
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Math 40
Prealgebra
Section 7.3 – General Applications of Percent
Example 2: Erin answered 85% of the questions on her History exam correctly. If she had 34 correct answers,
how many questions were on her exam?
Solution: We need to find total amount of exam questions. We are given the amount of correct answers and
the percent of correct answers.
From this we have,
The amount of __________  % of __________ Total
The amount of correct answers = % of correct answers
Total
1) Identify a variable.
t  the total amount of questions
2) Write an equation.
The amount of __________  % of __________ Total
The amount of correct answers = % of correct answers Total
34
0.85
t
34  0.85 t
3)
4)
5)
Solve the equation.
34  0.85 t Divide both sides by 0.85 to solve for t
34
0.85t

0.85 0.85
40  t
State your answer.
There were 40 questions on Erin’s History exam.
Check your answer.
Does the answer makes sense? Yes!
Did you answer what the problem is asking for? Yes!
You Try It 2: Misty answered 90% of the questions on her Prealgebra exam correctly. If Misty had 27 correct
answers, how many questions were on her exam?
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Math 40
Prealgebra
Section 7.3 – General Applications of Percent
Example 3: Joanna answered 30 of 40 possible questions on her Sociology exam correctly. What percent of
the total number of questions did Joanna mark correctly?
Solution: We need to find the percent of correct answers. We are given the amount of correct answers and
the total number of questions.
From this we have,
The amount of __________  % of __________ Total
The amount of correct answers = % of correct answers
Total
1) Identify a variable.
p  the percentage of correct answers
2) Write an equation.
The amount of __________  % of __________ Total
The amount of correct answers = % of correct answers Total
30
p
40
30  p 40
3)
Solve the equation.
30  p 40 Divide both sides by 40 to solve for p
30 40 p

40 40
0.75  p
4) State your answer.
Don’t forget, the question asks you to find a percent, you need to change the decimal into a
percent before stating your answer.
JoAnna marked 75% of the exam questions correct on her Sociology exam.
5) Check your answer.
Does the answer makes sense? Yes!
Did you answer what the problem is asking for? Yes!
You Try It 3: Lester answered 19 of 25 questions on his Biology exam correctly. What percent of the questions
did he mark correctly?
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Math 40
Prealgebra
Section 7.3 – General Applications of Percent
Example 4: 35 milliliters of a 60 milliliter solution is hydrochloric acid. What percent of the solution is
hydrochloric acid? Round your answer to the nearest tenth of a percent.
Solution: We need to find the percent of hydrochloric acid in the solution. We are given the number of
milliliters of hydrochloric acid and the total number of milliliters in the solution.
From this we have,
The amount of __________  % of __________ Total
The amount of milliliters of hydrochloric acid = % of milliliters of hydrochloric acid
Total
1) Identify a variable.
h  the percentage of milliliters of hydrochloric acid
2) Write an equation.
The amount of __________  % of __________ Total
The amount of milliliters of hydrochloric acid = % of milliliters of hydrochloric acid Total
35
h
60
35  h 60
3)
Solve the equation.
35  h 60 Divide both sides by 60 to solve for h
35 60h

60 60
0.583  h
4) State your answer.
Don’t forget, the question asks you to find a percent, you need to change the decimal into a
percent before stating your answer. Since this question asks us to round to the nearest tenth of a
percent, we change the decimal to a percent first and then round accordingly.
0.583  58.3%  58.33333 %  58.3%
The solution is approximately 58.3% hydrochloric acid.
5) Check your answer.
Does the answer makes sense? Yes!
Did you answer what the problem is asking for? Yes!
You Try It 4: 25 milliliters of a 40 milliliter solution is sulfuric acid. What percent of the solution is sulfuric
acid?
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