Learning Objectives
By the end of this section, you will be able to:
- Translate and solve basic percent equations
- Solve applications of percent
- Find percent increase and percent decrease
Before you get started, take this readiness quiz.
Translate and solve: of is
If you missed this problem, review Example 4.105.
Simplify:
If you missed this problem, review Example 5.15.
Solve:
If you missed this problem, review Example 5.43.
Translate and Solve Basic Percent Equations
We will solve percent equations by using the methods we used to solve equations with fractions or decimals. 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 as a prealgebra student, 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 They wanted to leave a tip. What amount would the tip be?
To solve this, we want to find what amount is of The is called the base. The amount of the tip would be or See Figure 6.6. To find the amount of the tip, we multiplied the percent by the base.
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.
Example 6.14
What number is of
What number is of
What number is of
Example 6.15
of is what number?
of is what number?
of is what number?
In the next examples, we are asked to find the base.
Example 6.16
Translate and solve: is of what number?
is of what number?
is of what number?
Example 6.17
of what number is
of what number is
of what number is
In the next examples, we will solve for the percent.
Example 6.18
What percent of is
What percent of is
What percent of is
Example 6.19
is what percent of
is what percent of
is what percent of
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.
How To
Solve an application
- Step 1. Identify what you are asked to find and choose a variable to represent it.
- Step 2. Write a sentence that gives the information to find it.
- Step 3. Translate the sentence into an equation.
- Step 4. Solve the equation using good algebra techniques.
- Step 5. Check the answer in the problem and make sure it makes sense.
- Step 6. Write a complete sentence that answers the question.
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.
Example 6.20
Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was They want to leave an tip. If the tip will be of the total bill, how much should the tip be?
Cierra and her sister enjoyed a special dinner in a restaurant, and the bill was If she wants to leave of the total bill as her tip, how much should she leave?
Kimngoc had lunch at her favorite restaurant. She wants to leave of the total bill as her tip. If her bill was how much will she leave for the tip?
Example 6.21
The label on Masao's breakfast cereal said that one serving of cereal provides milligrams (mg) of potassium, which is of the recommended daily amount. What is the total recommended daily amount of potassium?
One serving of wheat square cereal has grams of fiber, which is of the recommended daily amount. What is the total recommended daily amount of fiber?
One serving of rice cereal has mg of sodium, which is of the recommended daily amount. What is the total recommended daily amount of sodium?
Example 6.22
Mitzi received some gourmet brownies as a gift. The wrapper said each brownie was calories, and had calories of fat. What percent of the total calories in each brownie comes from fat?
Veronica is planning to make muffins from a mix. The package says each muffin will be calories and calories will be from fat. What percent of the total calories is from fat? (Round to the nearest whole percent.)
The brownie mix Ricardo plans to use says that each brownie will be calories, and calories are from fat. What percent of the total calories are from fat?
Find Percent Increase and Percent Decrease
People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.
To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.
How To
Find Percent Increase.
Step 1. Find the amount of increase.
Step 2. Find the percent increase as a percent of the original amount.
Example 6.23
In the California governor proposed raising community college fees from per unit to per unit. Find the percent increase. (Round to the nearest tenth of a percent.)
In the IRS increased the deductible mileage cost to cents from cents. Find the percent increase. (Round to the nearest tenth of a percent.)
In the standard bus fare in Chicago was In the standard bus fare was Find the percent increase. (Round to the nearest tenth of a percent.)
Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.
How To
Find percent decrease.
- Step 1. Find the amount of decrease.
- Step 2. Find the percent decrease as a percent of the original amount.
Example 6.24
The average price of a gallon of gas in one city in June was The average price in that city in July was Find the percent decrease.
The population of one city was about in The population of the city is projected to be about in Find the percent decrease. (Round to the nearest tenth of a percent.)
Last year Sheila's salary was Because of furlough days, this year her salary was Find the percent decrease. (Round to the nearest tenth of a percent.)
Media Access Additional Online Resources
Section 6.2 Exercises
Practice Makes Perfect
Translate and Solve Basic Percent Equations
In the following exercises, translate and solve.
What number is of
What number is of
of is what number?
of is what number?
is of what number?
is of what number?
of what number is
of what number is
What percent of is
What percent of is
is what percent of
is what percent of
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 She wants to leave of the total bill as a tip. How much should the tip be?
When Hiro and his co-workers had lunch at a restaurant the bill was They want to leave of the total bill as a tip. How much should the tip be?
Trong has of each paycheck automatically deposited to his savings account. His last paycheck was How much money was deposited to Trong's savings account?
Cherise deposits of each paycheck into her retirement account. Her last paycheck was How much did Cherise deposit into her retirement account?
One serving of oatmeal has grams of fiber, which is of the recommended daily amount. What is the total recommended daily amount of fiber?
One serving of trail mix has grams of carbohydrates, which is of the recommended daily amount. What is the total recommended daily amount of carbohydrates?
A bacon cheeseburger at a popular fast food restaurant contains milligrams (mg) of sodium, which is of the recommended daily amount. What is the total recommended daily amount of sodium?
A grilled chicken salad at a popular fast food restaurant contains milligrams (mg) of sodium, which is 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 calories, and calories are from fat. What percent of the total calories is from fat?
The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has calories, and calories are from fat. What percent of the total calories is from fat?
Emma gets paid per month. She pays a month for rent. What percent of her monthly pay goes to rent?
Dimple gets paid per month. She pays a month for rent. What percent of her monthly pay goes to rent?
Find Percent Increase and Percent Decrease
In the following exercises, find the percent increase or percent decrease.
Ayodele got a raise in her hourly pay, from to Find the percent increase.
Annual student fees at the University of California rose from about in to about in Find the percent increase.
The price of a share of one stock rose from to Find the percent increase.
According to Time magazine annual global seafood consumption rose from pounds per person in to pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)
In one month, the median home price in the Northeast rose from to Find the percent increase. (Round to the nearest tenth of a percent.)
The price of a share of one stock fell from to Find the percent decrease.
From to the population of Detroit fell from about to about Find the percent decrease. (Round to the nearest tenth of a percent.)
In one month, the median home price in the West fell from to Find the percent decrease. (Round to the nearest tenth of a percent.)
Sales of video games and consoles fell from million to million in one year. Find the percent decrease. (Round to the nearest tenth of a percent.)
Everyday Math
Tipping At the campus coffee cart, a medium coffee costs MaryAnne brings with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?
Late Fees Alison was late paying her credit card bill of She was charged a late fee. What was the amount of the late fee?
Writing Exercises
Without solving the problem is of what number”, think about what the solution might be. Should it be a number that is greater than or less than Explain your reasoning.
Without solving the problem “What is of think about what the solution might be. Should it be a number that is greater than or less than Explain your reasoning.
After returning from vacation, Alex said he should have packed fewer shorts and more shirts. Explain what Alex meant.
Because of road construction in one city, commuters were advised to plan their Monday morning commute to take of their usual commuting time. Explain what this means.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After reviewing this checklist, what will you do to become confident for all objectives?