In the previous section, you used a percent bar and the percent proportion to represent the relationship among the part, whole, and percent for a given problem situation. For example, consider the problem below, the percent bar that can be used to represent the problem, and the percent proportion that can be used to determine the exact solution to the problem.

In this section, you will use what you know about percent bars and the percent proportion to solve application problems involving percents.

Part 1: Finding the Part

Consider the problem below.

Mr. Martinez is giving a 60 question final exam in his social studies classroom. Steve figures that he needs to answer 75% of the questions correctly in order to pass the semester. How many questions does Steve need to answer correctly in order to pass the semester?

Use the information in the problem to set up a percent bar to estimate the solution.

Drag the tiles to create a percent proportion that can be used to determine the exact solution to the problem.

Use your percent bar and percent proportion to answer the following questions.

• How many questions does Steve need to answer correctly in order to pass?

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  Check Your Answer

  Steve needs to answer 45 questions correctly in order to pass.

• How is the way that the solution is represented in the percent bar similar to the way the solution is represented in the percent proportion? How is it different?

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  Check Your Answer

  Both the percent bar and percent proportion represent the ratio of the part (number of questions Steve must answer correctly) to the whole (total number of questions on the exam). The percent bar is a pictorial representation, and the percent proportion is a numerical representation of the same ratio.

Part 2: Finding the Percent

Consider the problem below.

In September 2014, the two states that produced the most crude oil were Texas and North Dakota. Texas produced 97.6 million barrels of oil and North Dakota produced 35.5 million barrels of oil. The entire oil production for the United States in September 2014 was 265.3 million barrels of oil. What percent of the oil produced in the United States was produced in Texas?

Use the information in the problem to set up a percent bar to estimate the solution.

Drag the tiles to create a percent proportion that can be used to determine the exact solution to the problem.

Use your percent bar and percent proportion to answer the following questions.

• What percent of the U.S. oil production for September 2014 was produced in Texas?

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  Check Your Answer

  About 36.8% of the total U.S. oil production was produced in Texas.

• How is the way that the solution is represented in the percent bar similar to the way the solution is represented in the percent proportion? How is it different?

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  Check Your Answer

  Both the percent bar and percent proportion represent the ratio of the part (number of barrels of oil produced in Texas) to the whole (total number of barrels of oil produced in the U.S.). The percent bar is a pictorial representation, and the percent proportion is a numerical representation of the same ratio.

Part 3: Finding the Whole

Consider the problem below.

In December 2014, there were 380,000 acre-feet of water in Lake Lewisville, which is 67.5% full. What is the capacity of Lake Lewisville in acre-feet when it is completely full?

Use the information in the problem to set up a percent bar to estimate the solution.

Drag the tiles to create a percent proportion that can be used to determine the exact solution to the problem.

Use your percent bar and percent proportion to answer the following questions.

• What is the total capacity of Lake Lewisville, or the amount of water that it will hold when completely full?

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  Check Your Answer

  About 563,000 acre-feet

• How is the way that the solution is represented in the percent bar similar to the way the solution is represented in the percent proportion? How is it different?

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  Check Your Answer

  Both the percent bar and percent proportion represent the ratio of the part (current amount of water in Lake Lewisville) to the whole (total capacity of Lake Lewisville). The percent bar is a pictorial representation and the percent proportion is a numerical representation of the same ratio.

Pause and Reflect

How can you use a percent bar and a percent proportion to solve a problem involving percents?

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Check Your Answer

Identify the information that you are given in a problem, which is typically two of the three pieces of information describing a percent: the part, the whole, and the percent. Use a percent bar to illustrate the ratio of the part to the whole and its equivalent ratio in terms of parts per 100 (percent). Use the percent proportion to write two equivalent ratios.

Practice

1. A report from the U.S. Department of Energy listed the oil imports for July of 2011. In July 2011, the United States purchased an average of about 9 million barrels of oil from other countries every day. The greatest number of barrels of oil purchased was from Canada. If the oil purchased from Canada represents 24% of the total purchased, how many barrels of oil did the U.S. buy from Canada each day?

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   Need a hint?

   Identify the percent, part, and whole from the problem. Set up and solve a percent proportion.
   
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   Check Your Answer

   2.16 million barrels of oil were purchased from Canada each day.
2. In a large school district in Texas, there were 46,000 students enrolled in the district. Of those, 6,200 were African-American and 9,660 were Asian-American. What percent of the district’s students were Asian-American?

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   Need a hint?

   Identify the percent, part, and whole from the problem. Set up and solve a percent proportion.
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   Check Your Answer

   21% of the students in this district were Asian-American.
3. In 2013, the population of Chicago was about 2.7 million people, which is 21% of the total population of the state of Illinois. About how many people live in Illinois?

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   Identify the percent, part, and whole from the problem. Set up and solve a percent proportion.
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   Check Your Answer

   About 12.9 million people live in Illinois.