Chapter 7—Percents
7-3 Solving Percent Problems
When you complete the work for this section, you should be able to: - Identify the three basic parts of a percentage problem: amount, base, and percent.
- Determine the percent, given the amount and base.
- Determine the amount, given the percent and base.
- Determine the base, given the percent and amount.
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There are just three parts to a percentage problem: the amount, the percent, and the base. Here is how those three parts fit together:
- The amount and base are parts of a fraction:
- The percent is found by converting this fraction to a percent.
Once you get these relationships clearly in mind, you will be able to solve problems such as these:
- There are 27 men and 32 women in the new class. What percent of the class is female?
- A $140 suit is on sale at 12% off. What is the actual sale price?
- A salesman receives 12.5% of the sale price of a used car. If he is receives $180 on a certain sale, what is the price of the car?
Finding the Percent in Percent Problems
In problems of this type, you are given the amount and base, and your job is to find the percent:
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What percent of the balls are red?  What percent of the balls are blue?  |
Example 1
Problem 128 is _____ % of 1280 | |
| Procedure | |
Identify the base and amount. | Amount = 128
Base = 1280 |
Solve: | 128/1280 x 100 = 10% |
Solution 128 is 10% of 1280 | |
Example 2
Problem Kevin works 12 hours out of each weekday. What percentage of those days does he work? | |
| Procedure | |
Identify the base and amount. | Amount = 12 hours
Base = 24 hours per day |
Solve: | 12/24 x 100 = 50% |
Solution When Kevin works 12 hours in a day, he works 50% of that day. | |
Example 3
Problem Three out of 120 students in my graduating class have red hair. What percentage of this class is redheads? | |
| Procedure | |
Identify the base and amount. | Amount = 120
Base = 3 |
Solve: | 3/120 x 100 = 2.5% |
Solution The percentage of people with red hair in this class is 2.5% | |
Examples and Exercises
Finding Percentage Determine the percentage, given the base and amount. Round the percentage to the nearest tenth where necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Finding the Amount in Percent Problems
In problems of this type, you are given the base and percent, and you are expected to find the amount.
These problems often look something like this: 20% of the marbles in a bag are blue. If there are 70 marbles in the bag, how many are blue? You know the percent (20%) and the base (70 marbles). So the amount is found by:
= 14 blue marbles
So there are 14 blue marbles in the bag. By the way, how many marbles are a color different from blue? The simplest way to find the answer is to subtract the number of blue marbles from the total number of marbles in the bag: 70 – 14 = 56 marbles that aren't blue.
Example 4
Problem 15% of 60 is _____ | |
| Procedure | |
Identify the base and percent. | Base = 60
Percent = 15 |
Solve: | (60 x 15) / 100 = 9 |
Solution 15% of 60 is 9 | |
Example 5
Problem If 10% of the candies in a package of M&Ms are red, how many red candies can you expect to find in a package containing a total of 28 M&M? Round your answer to the next-higher whole-number value. | |
| Procedure | |
Identify the base and percent. | Base = 28
Percent = 10 |
Solve: | (28 x 10) / 100 = 2.8 or 3. |
Solution If 10% of the M&Ms in a package are red and you have a package of 28 M&Ms, you can expect to find only about 3 red candies. | |
One of the most common applications of this kind of percent problem is finding the sale price of an item that is marked down a given percent. The problem is usually given in these terms: A business is offering 20% off every item in the store. How much will you pay for a $98.00 desk set? Be careful, however. You can find that 20% of $98.00 is $19.60, but that isn't the sale price. That is the amount that is taken from the usual price. So to find the actual sale price, you must subtract the "amount off" from the usual price: $98.00 – $19.60 = $78.40. The sale price is $78.40.
Example 6
Problem A suit that normally sells for $184.90 is on sale today at 12% off. What is the sale price of the suit? Round your final answer up to the nearest cent. | |
| Procedure | |
Identify the base and percent. | Base = 184.90
Percent = 12 |
Find the amount to be taken from the full price: | (184.90 x 12) / 100 = $22.188 |
Subtract the amount of reduction from the full price. | Sale price = $184.90 – $2.188 = $162.712 or $162.72 |
Solution The sale price of $184.90 suit that is marked down 12% will sell for $162.72. | |
Examples and Exercises
Finding the Amount Determine the amount, given the base and percentage. Round the answer to the nearest tenth where necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Finding the Base in Percent Problems
In problems of this type, you are given the amount and percent, and then asked to find the base.
Example 7
Problem 22 is 12% of _____ | |
| Procedure | |
Identify the amount and percent. | Amount = 22
Percent = 12 |
Solve: | 22/12 x 100 = 183.3 |
Solution 22 is 12% of 183.3 | |
Examples and Exercises
Finding the Amount Determine the amount, given the base and percentage. Round the answer to the nearest tenth where necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Lesson Summary
Exercises Solve these percentage problem. Continue until you achieve consistent, correct results. | |
