3.1.6: Applications of Percents

Learning Objectives

• be able to distinguish between base, percent, and percentage
• be able to find the percentage, the percent, and the base

Base, Percent, and Percentage

There are three basic types of percent problems. Each type involves a base, a percent, and a percentage, and when they are translated from words to mathemati­cal symbols each becomes a multiplication statement. Examples of these types of problems are the following:

1. What number is 30% of 50? (Missing product statement.)
2. 15 is what percent of 50? (Missing factor statement.)
3. 15 is 30% of what number? (Missing factor statement.)

In problem 1, the product is missing. To solve the problem, we represent the missing product with \(P\).

\(P = 30\% \cdot 50\)

Definition: Percentage

The missing product \(P\) is called the percentage. Percentage means part, or por­tion. In \(P = 30\% \cdot 50\). \(P\) represents a particular part of 50.

In problem 2, one of the factors is missing. Here we represent the missing factor with \(Q\).

\(15 = Q \cdot 50\)

Percent
The missing factor is the percent. Percent, we know, means per 100, or part of 100. In \(15 = Q \cdot 50\). \(Q\) indicates what part of 50 is being taken or considered. Specifi­cally, \(15 = Q \cdot 50\) means that if 50 was to be divided into 100 equal parts, then \(Q\) indicates 15 are being considered.

In problem 3, one of the factors is missing. Represent the missing factor with \(B\).

\(15 = 30\% \cdot B\)

Base
The missing factor is the base. Some meanings of base are a source of supply, or a starting place. In \(15 = 30\% \cdot B\), \(B\) indicates the amount of supply. Specifically, \(15 = 30\% \cdot B\) indicates that 15 represents 30% of the total supply.

Each of these three types of problems is of the form

\(\text{(percentage)} = \text{(percent)} \cdot \text{(base)}\)

We can determine any one of the three values given the other two using the methods discussed in [link].

Finding the Percentage

Sample Set A

\(\begin{array} {cccccl} {\text{What number}} & {\text{is}} & {30\%} & {\text{of}} & {50?} & {\text{Missing product statement.}} \\ {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {P} & {=} & {30\%} & {\cdot} & {50} & {\text{Convert 30% to a decimal.}} \\ {P} & {=} & {.30} & {\cdot} & {50} & {\text{Multiply.}} \\ {P} & {=} & {15} & {} & {} & {} \end{array}\)

Thus, 15 is 30% of 50.

Sample Set A

\(\begin{array} {cccccl} {\text{What number}} & {\text{is}} & {36\%} & {\text{of}} & {95?} & {\text{Missing product statement.}} \\ {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {P} & {=} & {36\%} & {\cdot} & {95} & {\text{Convert 36% to a decimal.}} \\ {P} & {=} & {.36} & {\cdot} & {95} & {\text{Multiply.}} \\ {P} & {=} & {34.2} & {} & {} & {} \end{array}\)

Thus, 34.2 is 36% of 95.

Sample Set A

A salesperson, who gets a commission of 12% of each sale she makes, makes a sale of $8,400.00. How much is her commission?

Solution

We need to determine what part of $8,400.00 is to be taken. What part indicates percentage.

\(\begin{array} {cccccl} {\text{What number}} & {\text{is}} & {12\%} & {\text{of}} & {8,400.00?} & {\text{Missing product statement.}} \\ {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {P} & {=} & {12\%} & {\cdot} & {8,400.00} & {\text{Convert to decimals.}} \\ {P} & {=} & {.12} & {\cdot} & {8,400.00} & {\text{Multiply.}} \\ {P} & {=} & {1008.00} & {} & {} & {} \end{array}\)

Thus, the salesperson's commission is $1,008.00.

Sample Set A

A girl, by practicing typing on her home computer, has been able to increase her typing speed by 110%. If she originally typed 16 words per minute, by how many words per minute was she able to increase her speed?

Solution

We need to determine what part of 16 has been taken. What part indicates percentage.

\(\begin{array} {cccccl} {\text{What number}} & {\text{is}} & {110\%} & {\text{of}} & {16?} & {\text{Missing product statement.}} \\ {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {P} & {=} & {110\%} & {\cdot} & {16} & {\text{Convert to decimals.}} \\ {P} & {=} & {1.10} & {\cdot} & {16} & {\text{Multiply.}} \\ {P} & {=} & {17.6} & {} & {} & {} \end{array}\)

Thus, the girl has increased her typing speed by 17.6 words per minute. Her new speed is \(16 + 17.6 = 33.6\) words per minute.

Sample Set A

A student who makes $125 a month working part-time receives a 4% salary raise. What is the student's new monthly salary?

Solution

With a 4% raise, this student will make 100% of the original salary + 4% of the original salary. This means the new salary will be 104% of the original salary. We need to determine what part of $125 is to be taken. What part indicates percentage.

\(\begin{array} {cccccl} {\text{What number}} & {\text{is}} & {104\%} & {\text{of}} & {125} & {\text{Missing product statement.}} \\ {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {P} & {=} & {104\%} & {\cdot} & {125} & {\text{Convert to decimals.}} \\ {P} & {=} & {1.04} & {\cdot} & {125} & {\text{Multiply.}} \\ {P} & {=} & {130} & {} & {} & {} \end{array}\)

Thus, this student's new monthly salary is $130.

Sample Set A

An article of clothing is on sale at 15% off the marked price. If the marked price is $24.95, what is the sale price?

Solution

Since the item is discounted 15%, the new price will be \(100\% - 15\% = 85\%\) of the marked price. We need to determine what part of 24.95 is to be taken. What part indicates percentage.

\(\begin{array} {cccccl} {\text{What number}} & {\text{is}} & {85\%} & {\text{of}} & {$24.95} & {\text{Missing product statement.}} \\ {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {P} & {=} & {85\%} & {\cdot} & {24.95} & {\text{Convert to decimals.}} \\ {P} & {=} & {.85} & {\cdot} & {24.95} & {\text{Multiply.}} \\ {P} & {=} & {21.2075} & {} & {} & {\text{Since this number represents money,}} \\ {} & {} & {} & {} & {} & {\text{we'll round to 2 decimal places}} \\ {P} & {=} & {21.21} & {} & {} & {} \end{array}\)

Thus, the sale price of the item is $21.21.

Practice Set A

What number is 42% of 85?

Answer

35.7

Practice Set A

A sales person makes a commission of 16% on each sale he makes. How much is his commission if he makes a sale of $8,500?

Answer

$1,360

Practice Set A

An assembly line worker can assemble 14 parts of a product in one hour. If he can increase his assembly speed by 35%, by how many parts per hour would he increase his assembly of products?

Answer

4.9

Practice Set A

A computer scientist in the Silicon Valley makes $42,000 annually. What would this scientist's new annual salary be if she were to receive an 8% raise?

Answer

$45,360

Finding the Percent

Sample Set B

\(\begin{array} {cccccl} {15} & {\text{is}} & {\text{What number}} & {\text{of}} & {50?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {[\text{(product)} = \text{(factor)} \cdot \text{(factor)}]} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {15} & {=} & {Q} & {\cdot} & {50} & {} \end{array}\)

Recall that (missing factor) = (product) \(\div\) (known factor).

\(\begin{array} {rccl} {Q} & = & {15 \div 50} & {\text{Divide.}} \\ {Q} & = & {0.3} & {\text{Convert to a percent}} \\ {Q} & = & {30\%} & {} \end{array}\)

Thus, 15 is 30% of 50.

Sample Set B

\(\begin{array} {cccccl} {4.32} & {\text{is}} & {\text{What percent}} & {\text{of}} & {72?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {[\text{(product)} = \text{(factor)} \cdot \text{(factor)}]} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {4.32} & {=} & {Q} & {\cdot} & {72} & {} \end{array}\)

\(\begin{array} {rccl} {Q} & = & {4.32 \div 72} & {\text{Divide.}} \\ {Q} & = & {0.06} & {\text{Convert to a percent}} \\ {Q} & = & {6\%} & {} \end{array}\)

Thus, 4.32 is 6% of 72.

Sample Set B

On a 160 question exam, a student got 125 correct answers. What percent is this? Round the result to two decimal places.

Solution

We need to determine the percent.

\(\begin{array} {cccccl} {125} & {\text{is}} & {\text{What percent}} & {\text{of}} & {160?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {[\text{(product)} = \text{(factor)} \cdot \text{(factor)}]} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {125} & {=} & {Q} & {\cdot} & {160} & {} \end{array}\)

\(\begin{array} {rccl} {Q} & = & {125 \div 160} & {\text{Divide.}} \\ {Q} & = & {0.78125} & {\text{Round to two decimal places}} \\ {Q} & = & {.78} & {} \end{array}\)

Thus, this student received a 78% on the exam.

Sample Set B

A bottle contains 80 milliliters of hydrochloric acid (HCl) and 30 milliliters of water. What percent of HCl does the bottle contain? Round the result to two decimal places.

Solution

We need to determine the percent. The total amount of liquid in the bottle is

\(\text{80 milliliters + 30 milliliters = 110 milliliters}\)

\(\begin{array} {cccccl} {80} & {\text{is}} & {\text{What percent}} & {\text{of}} & {110?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {[\text{(product)} = \text{(factor)} \cdot \text{(factor)}]} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {80} & {=} & {Q} & {\cdot} & {110} & {} \end{array}\)

\(\begin{array} {rccl} {Q} & = & {80 \div 110} & {\text{Divide.}} \\ {Q} & = & {0.727272...} & {\text{Round to two decimal places}} \\ {Q} & \approx & {73\%} & {\text{The symbol "} \approx \text{" is read as "approximately."}} \end{array}\)

Thus, this bottle contains approximately 73% HCl.

Sample Set B

Five years ago a woman had an annual income of $19,200. She presently earns $42,000 annually. By what percent has her salary increased? Round the result to two decimal places.

Solution

We need to determine the percent.

\(\begin{array} {cccccl} {42,000} & {\text{is}} & {\text{What percent}} & {\text{of}} & {19,200?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {42,000} & {=} & {Q} & {\cdot} & {19,200} & {} \end{array}\)

\(\begin{array} {rccl} {Q} & = & {42,000 \div 19,200} & {\text{Divide.}} \\ {Q} & = & {2.1875} & {\text{Round to two decimal places}} \\ {Q} & = & {2.19} & {\text{Convert to a percent.}} \\ {Q} & = & {219\%} & {\text{Convert to a percent.}} \end{array}\)

Thus, this woman's annual salary has increased 219%.

Practice Set B

99.13 is what percent of 431?

Answer

23%

Practice Set B

On an 80 question exam, a student got 72 correct answers. What percent did the student get on the exam?

Answer

90%

Practice Set B

A bottle contains 45 milliliters of sugar and 67 milliliters of water. What fraction of sugar does the bottle contain? Round the result to two decimal places (then express as a percent).

Answer

40%

Finding the Base

Sample Set C

\(\begin{array} {cccccl} {15} & {\text{is}} & {30\%} & {\text{of}} & {\text{What number}?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {[\text{(product)} = \text{(factor)} \cdot \text{(factor)}]} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {15} & {=} & {30\%} & {\cdot} & {B} & {\text{Convert to decimals.}} \\ {15} & {=} & {.30} & {\cdot} & {B} & {\text{[\text{(missing factor)} = \text{(product)} \div \text{(known factor)}]}} \end{array}\)

\(\begin{array} {rcl} {B} & = & {15 \div .30} \\ {B} & = & {50} \end{array}\)

Thus, 15 is 30% of 50.

Sample Set C

\(\begin{array} {cccccl} {56.43} & {\text{is}} & {33\%} & {\text{of}} & {\text{What number}?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {[\text{(product)} = \text{(factor)} \cdot \text{(factor)}]} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {56.43} & {=} & {33\%} & {\cdot} & {B} & {\text{Convert to decimals.}} \\ {56.43} & {=} & {.33} & {\cdot} & {B} & {\text{Divide.}} \end{array}\)

\(\begin{array} {rcl} {B} & = & {56.43 \div .33} \\ {B} & = & {171} \end{array}\)

Thus, 56.43 is 33% of 171.

Sample Set C

Fifteen milliliters of water represents 2% of a hydrochloric acid (HCl) solution. How many milliliters of solution are there?

Solution

We need to determine the total supply. The word supply indicates base.

\(\begin{array} {cccccl} {15} & {\text{is}} & {2\%} & {\text{of}} & {\text{What number}?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {[\text{(product)} = \text{(factor)} \cdot \text{(factor)}]} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {15} & {=} & {2\%} & {\cdot} & {B} & {\text{Convert to decimals.}} \\ {15} & {=} & {.02} & {\cdot} & {B} & {\text{Divide.}} \end{array}\)

\(\begin{array} {rcl} {B} & = & {15 \div .02} \\ {B} & = & {750} \end{array}\)

Thus, there are 750 milliliters of solution in the bottle.

Sample Set C

In a particular city, a sales tax of \(6 \dfrac{1}{2}\) % is charged on items purchased in local stores. If the tax on an item is $2.99, what is the price of the item?

Solution

We need to determine the price of the item. We can think of price as the starting place. Starting place indicates base. We need to determine the base.

\(\begin{array} {cccccl} {2.99} & {\text{is}} & {6 \dfrac{1}{2}\%} & {\text{of}} & {\text{What number}?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {2.99} & {=} & {6 \dfrac{1}{2}\%} & {\cdot} & {B} & {\text{Convert to decimals.}} \\ {2.99} & {=} & {6.5\%} & {\cdot} & {B} & {} \\ {2.99} & {=} & {0.065} & {\cdot} & {B} & {[\text{(missing factor)} = \text{(product)} \div \text{(known factor)}]} \end{array}\)

\(\begin{array} {rcll} {B} & = & {2.99 \div .065} & {\text{Divide.}} \\ {B} & = & {46} & {} \end{array}\)

Thus, the price of the item is $46.00.

Sample Set C

A clothing item is priced at $20.40. This marked price includes a 15% discount. What is the original price?

Solution

We need to determine the original price. We can think of the original price as the starting place. Starting place indicates base. We need to determine the base. The new price, $20.40, represents \(100\% - 15\% = 85\%\) of the original price.

\(\begin{array} {cccccl} {20.40} & {\text{is}} & {85\%} & {\text{of}} & {\text{What number}?} & {\text{Missing factor statement.}} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\underbrace{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }_{}}} & {} \\ {\text{(percentage)}} & {=} & {\text{(percent)}} & {\cdot} & {\text{(base)}} & {} \\ {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {^{\downarrow}} & {} \\ {20.40} & {=} & {85\%} & {\cdot} & {B} & {\text{Convert to decimals.}} \\ {20.40} & {=} & {0.85} & {\cdot} & {B} & {[\text{(missing factor)} = \text{(product)} \div \text{(known factor)}]} \end{array}\)

\(\begin{array} {rcll} {B} & = & {20.40 \div .85} & {\text{Divide.}} \\ {B} & = & {24} & {} \end{array}\)

Thus, the original price of the item is $24.00.

Practice Set C

1.98 is 2% of what number?

Answer

99

Practice Set C

3.3 milliliters of HCl represents 25% of an HCl solution. How many milliliters of solution are there?

Answer

13.2ml

Practice Set C

A salesman, who makes a commission of \(18 \dfrac{1}{4}\)% on each sale, makes a commission of $152.39 on a particular sale. Rounded to the nearest dollar, what is the amount of the sale?

Answer

$835

Practice Set C

At "super-long play," \(2\dfrac{1}{2}\) hours of play of a video cassette recorder represents 31.25% of the total playing time. What is the total playing time?

Answer

8 hours

Exercises

For the following 25 problems, find each indicated quantity.

Exercise \(\PageIndex{1}\)

What is 21% of 104?

Answer

21.84

Exercise \(\PageIndex{2}\)

What is 8% of 36?

Exercise \(\PageIndex{3}\)

What is 98% of 545?

Answer

534.1

Exercise \(\PageIndex{4}\)

What is 143% of 33?

Exercise \(\PageIndex{5}\)

What is \(10 \dfrac{1}{2}\)% of 20?

Answer

2.1

Exercise \(\PageIndex{6}\)

3.25 is what percent of 88?

Exercise \(\PageIndex{7}\)

22.44 is what percent of 44?

Answer

51

Exercise \(\PageIndex{8}\)

0.0036 is what percent of 0.03?

Exercise \(\PageIndex{9}\)

31.2 is what percent of 26?

Answer

120

Exercise \(\PageIndex{10}\)

266.4 is what percent of 74?

Exercise \(\PageIndex{11}\)

0.0101 is what percent of 0.0505?

Answer

20

Exercise \(\PageIndex{12}\)

2.4 is 24% of what number?

Exercise \(\PageIndex{13}\)

24.19 is 41% of what number?

Answer

59

Exercise \(\PageIndex{14}\)

61.12 is 16% of what number?

Exercise \(\PageIndex{15}\)

82.81 is 91% of what number?

Answer

91

Exercise \(\PageIndex{16}\)

115.5 is 20% of what number?

Exercise \(\PageIndex{17}\)

43.92 is 480% of what number?

Answer

9.15

Exercise \(\PageIndex{18}\)

What is 85% of 62?

Exercise \(\PageIndex{19}\)

29.14 is what percent of 5.13?

Answer

568

Exercise \(\PageIndex{20}\)

0.6156 is what percent of 5.13?

Exercise \(\PageIndex{21}\)

What is 0.41% of 291.1?

Answer

1.19351

Exercise \(\PageIndex{22}\)

26.136 is 121% of what number?

Exercise \(\PageIndex{23}\)

1,937.5 is what percent of 775?

Answer

250

Exercise \(\PageIndex{24}\)

1 is what percent of 2,000?

Exercise \(\PageIndex{25}\)

0 is what percent of 59?

Answer

0

Exercise \(\PageIndex{26}\)

An item of clothing is on sale for 10% off the marked price. If the marked price is $14.95, what is the sale price? (Round to two decimal places.)

Exercise \(\PageIndex{27}\)

A grocery clerk, who makes $365 per month, re­ceives a 7% raise. How much is her new monthly salary?

Answer

390.55

Exercise \(\PageIndex{28}\)

An item of clothing which originally sells for $55.00 is marked down to $46.75. What percent has it been marked down?

Exercise \(\PageIndex{29}\)

On a 25 question exam, a student gets 21 correct. What percent is this?

Answer

84

Exercise \(\PageIndex{30}\)

On a 45 question exam, a student gets 40%. How many questions did this student get correct?

Exercise \(\PageIndex{31}\)

A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C. What per­cent of the weight of this tablet is vitamin C?

Answer

14

Exercise \(\PageIndex{32}\)

Five years ago a secretary made $11,200 an­nually. The secretary now makes $17,920 an­nually. By what percent has this secretary's sal­ary been increased?

Exercise \(\PageIndex{33}\)

A baseball team wins \(48 \dfrac{3}{4}\)% of all their games. If they won 78 games, how many games did they play?

Answer

160

Exercise \(\PageIndex{34}\)

A typist was able to increase his speed by 120% to 42 words per minute. What was his original typ­ing speed?

Exercise \(\PageIndex{35}\)

A salesperson makes a commission of 12% on the total amount of each sale. If, in one month, she makes a total of $8,520 in sales, how much has she made in commission?

Answer

$1,022.40

Exercise \(\PageIndex{36}\)

A salesperson receives a salary of $850 per month plus a commission of \(8\dfrac{1}{2}\) % of her sales. If, in a particular month, she sells $22,800 worth of merchandise, what will be her monthly earn­ings?

Exercise \(\PageIndex{37}\)

A man borrows $1150.00 from a loan company. If he makes 12 equal monthly payments of $130.60, what percent of the loan is he paying in interest?

Answer

36.28%

Exercise \(\PageIndex{38}\)

The distance from the sun to the earth is approx­imately 93,000,000 miles. The distance from the sun to Pluto is approximately 860.2% of the dis­tance from the sun to the Earth. Approximately, how many miles is Pluto from the sun?

Exercise \(\PageIndex{39}\)

The number of people on food stamps in Maine in 1975 was 151,000. By 1980, the number had decreased to 59,200. By what percent did the number of people on food stamps decrease? (Round the result to the nearest percent.)

Answer

61

Exercise \(\PageIndex{40}\)

In Nebraska, in 1960, there were 734,000 motor-vehicle registrations. By 1979, the total had in­creased by about 165.6%. About how many motor-vehicle registrations were there in Ne­braska in 1979?

Exercise \(\PageIndex{41}\)

From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?

Answer

19,500

Exercise \(\PageIndex{42}\)

In 1950, in the United States, there were 1,894 daily newspapers. That number decreased to 1,747 by 1981. What percent did the number of daily newspapers decrease?

Exercise \(\PageIndex{43}\)

A particular alloy is 27% copper. How many pounds of copper are there in 55 pounds of the alloy?

Answer

14.85

Exercise \(\PageIndex{44}\)

A bottle containing a solution of hydrochloric acid (HCl) is marked 15% (meaning that 15% of the HCl solution is acid). If a bottle contains 65 milliliters of solution, how many milliliters of water does it contain?

Exercise \(\PageIndex{45}\)

A bottle containing a solution of HCl is marked 45%. A test shows that 36 of the 80 milliliters contained in the bottle are hydrochloric acid. Is the bottle marked correctly? If not, how should it be remarked?

Answer

Marked correctly

Exercises For Review

Exercise \(\PageIndex{46}\)

Use the numbers 4 and 7 to illustrate the commutative property of multiplication.

Exercise \(\PageIndex{47}\)

Convert \(\dfrac{14}{5}\) to a mixed number.

Answer

\(2\dfrac{4}{5}\)

Exercise \(\PageIndex{48}\)

Arrange the numbers \(\dfrac{7}{12}\), \(\dfrac{5}{9}\) and \(\dfrac{4}{7}\) in increasing order.

Exercise \(\PageIndex{49}\)

Convert 4.006 to a mixed number.

Answer

\(4 \dfrac{3}{500}\)

Exercise \(\PageIndex{50}\)

Convert \(\dfrac{7}{8}\)% to a fraction.