Corequisite Skills for Introductory StatisticsXYZ Homework Edition

1.5 Finding a Percent of a Total

Narrated lesson: Finding a Percent of a Total

Synthetic narration with English captions, a transcript, and time to think before checking the answer.

Translate and Solve Basic Percent Equations

We will solve percent equations using algebra. In the past, you may have solved percent problems by setting them up as proportions. That was the best method available when you did not have the tools of algebra. Now you can translate word sentences into algebraic equations, and then solve the equations.

We'll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application.

When Aolani and her friends ate dinner at a restaurant, the bill came to $80. They wanted to leave a 20% tip. What amount would the tip be?

To solve this, we want to find what amount is 20% of $80. The $80 is called the base. The amount of the tip would be 0.20(80), or $16 See Figure 1.11. To find the amount of the tip, we multiplied the percent by the base.

The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.
The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.
Figure 1.11 A 20% tip for an $80 restaurant bill comes out to $16.

In the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.

In the next examples, we are asked to find the base.

In the next examples, we will solve for the percent.

Solve Applications of Percent

Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.

We will update the strategy we used in our earlier applications to include equations now. Notice that we will translate a sentence into an equation.

Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we'll solve involve everyday situations, you can rely on your own experience.

Practice Makes Perfect

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What number is 45% of 120?

Show solution

54

What number is 65% of 100?

What number is 24% of 112?

Show solution

26.88

What number is 36% of 124?

250% of 65 is what number?

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162.5

150% of 90 is what number?

800% of 2,250 is what number?

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18,000

600% of 1,740 is what number?

28 is 25% of what number?

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112

36 is 25% of what number?

81 is 75% of what number?

Show solution

108

93 is 75% of what number?

8.2% of what number is $2.87?

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$35

6.4% of what number is $2.88?

11.5% of what number is $108.10?

Show solution

$940

12.3% of what number is $92.25?

What percent of 260 is 78?

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30%

What percent of 215 is 86?

What percent of 1,500 is 540?

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36%

What percent of 1,800 is 846?

30 is what percent of 20?

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150%

50 is what percent of 40?

840 is what percent of 480?

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175%

790 is what percent of 395?

Solve Applications of Percents

In the following exercises, solve the applications of percents.

Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. She wants to leave 16% of the total bill as a tip. How much should the tip be?

Show solution

$11.88

When Hiro and his co-workers had lunch at a restaurant the bill was $90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?

Trong has 12% of each paycheck automatically deposited to his savings account. His last paycheck was $2,165. How much money was deposited to Trong's savings account?

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$259.80

Cherise deposits 8% of each paycheck into her retirement account. Her last paycheck was $1,485. How much did Cherise deposit into her retirement account?

One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber? Round to the nearest tenth of a gram.

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24.2 grams

One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

A bacon cheeseburger at a popular fast food restaurant contains 2,070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium? Round to the nearest milligram.

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2,407 mg

A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?

The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?

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45%

The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?

Emma gets paid $3,000 per month. She pays $750 a month for rent. What percent of her monthly pay goes to rent?

Show solution

25%

Dimple gets paid $3,200 per month. She pays $960 a month for rent. What percent of her monthly pay goes to rent?

Corequisite Skills for Introductory Statistics is a custom course edition compiled for Introductory Statistics corequisite courses from OpenStax Contemporary Mathematics, Elementary Algebra 2e, Intermediate Algebra 2e, Prealgebra 2e. Content by OpenStax is reproduced as published, apart from any corrections recorded for this edition. Sections are renumbered to follow the course outline. The course outline is adapted from Larry Green's Support Course for Elementary Statistics (LibreTexts, https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Support_Course_for_Elementary_Statistics), used under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Lessons 2.4 and 6.7 are written for this edition by XYZ Homework. Every OpenStax lesson is abridged to the subsections and practice exercises this course uses. Lessons are headed with their course titles, not the source section titles. Access the complete originals free at openstax.org. License: CC-BY-NC-SA-4.0.

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