Lauretta J. Fox
Problems involving percent are called percentage problems. Three of the most common types of percentage problems are (1) finding a percent of a given number, (2) finding what percent one number is of another, and (3) finding a number when a percent of it is given.
Any of these percentage problems may be solved in the following manner. Read the problem carefully to determine what is being asked. Represent the number that you wish to find by the letter N, and change the percent to a fraction. Let the word “of” denote multiplication. Translate the problem into a mathematical sentence, and solve the resulting equation to find the desired number N.
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Example 1:
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Find 6% of 80.
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Solution:
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Let N represent the required number.
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Change 6% to 6/100.
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Let the word “of” denote multiplication.
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N =6/100 x 80/1
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N= 480/100
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N= 4.80
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6% of 80 = 4.80
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Example 2:
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16 is what percent of 48?
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Solution:
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Let N represent the required percent.
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Change N% to N/100.
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Let the word “of” denote multiplication,
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16/1= N/100 x 48/1
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16/1= 48N/100
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48N = 1600
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N = 33 1/3
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16 is 33 1/3% of 48.
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Example 3:
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12 is 75% of what number?
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Solution:
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Let N represent the required number.
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Change 75% to 75/100.
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Let the word “of” denote multiplication.
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12/1= 75/100 x N/1
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12/1 75N/100
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75N =1200
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N =16
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12 is 75% of 16.
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Another common type of percentage problem is to find what percent greater or smaller one number is than another. To solve a problem ofthis type, use the following procedure. (1) Subtract to find the difference between the two numbers. (2) Compare the difference with the original number before it was increased or decreased. Do this by placing the difference in the numerator of a fraction whose denominator is the original number. (3) Multiply the fraction by one hundred to obtain the required rate of percent.
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Example 4:
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What percent greater than 75 is 100?
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Solution:
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100 75= 25
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25/75 1/3
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1/3 x 100/1 =100/3 = 33 1/3%
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100 is 33 1/3% greater than 75.
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Solve the following set of problems.
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1. 18% of 750 is ___.
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2. 86 is ___% of 129.
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3. 9 1/4% of 112 is ___.
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4. 45 is 90% of ___.
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5. 7 is ___% of 56.
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6. 3 is 7.5% of ___.
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7. 3.6% of 248 is ___.
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8. 15 is ___% of 60.
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9. Last month gasoline sold for $1.10 per gallon. This month it is selling for $1.32 per gallon. Find the percent of increase in the price per gallon.
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10. There are 180 days in the school year. Mary was present 95% of the total days. How many days was she present?
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11. On an arithmetic test John received a grade of 80%. He solved 24 problems correctly. How many problems were there on the test?
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12. Mr. Brown receives a weekly salary of $200. He spends $60 per week for food. What percent of his weekly salary does he use for food?
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13. Last year City High School had an enrollment of 1800 students. This year the enrollment is 1600 students. What is the percent of decrease in the student population?
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14. A number changed from 24 to 36. What was the percent of increase in the number? Later the number changed from 36 to 24. What was the percent of decrease in the number?
