# Lesson 11

Percentages and Double Number Lines

Let’s use double number lines to represent percentages.

Each of three friends—Lin, Jada, and Andre—had the goal of raising \$40. How much money did each person raise? Be prepared to explain your reasoning. 1. Lin raised 100% of her goal. 2. Jada raised 50% of her goal. 3. Andre raised 150% of his goal. ### 11.2: Three-Day Biking Trip Elena biked 8 miles on Saturday. Use the double number line to answer the questions. Be prepared to explain your reasoning. 1. What is 100% of her Saturday distance? 2. On Sunday, she biked 75% of her Saturday distance. How far was that? 3. On Monday, she biked 125% of her Saturday distance. How far was that? ### 11.3: Puppies Grow Up 1. Jada has a new puppy that weighs 9 pounds. The vet says that the puppy is now at about 20% of its adult weight. What will be the adult weight of the puppy? 2. Andre also has a puppy that weighs 9 pounds. The vet says that this puppy is now at about 30% of its adult weight. What will be the adult weight of Andre’s puppy? 3. What is the same about Jada and Andre’s puppies? What is different? A loaf of bread costs$2.50 today. The same size loaf cost 20 cents in 1955.

1. What percentage of today’s price did someone in 1955 pay for bread?
2. A job pays \$10.00 an hour today. If the same percentage applies to income as well, how much would that job have paid in 1955? ### Summary We can use a double number line to solve problems about percentages. For example, what is 30% of 50 pounds? We can draw a double number line like this: We divide the distance between 0% and 100% and that between 0 and 50 pounds into ten equal parts. We label the tick marks on the top line by counting by 5s ($$50 \div 10 = 5$$) and on the bottom line counting by 10% ($$100 \div 10 =10$$). We can then see that 30% of 50 pounds is 15 pounds. We can also use a table to solve this problem. Suppose we know that 140% of an amount is \$28. What is 100% of that amount? Let’s use a double number line to find out.

We divide the distance between 0% and 140% and that between \$0 and \$28 into fourteen equal intervals. We label the tick marks on the top line by counting by 2s and on the bottom line counting by 10%. We would then see that 100% is \\$20.

Or we can use a table as shown.

### Glossary Entries

• percent

The word percent means “for each 100.” The symbol for percent is %.

For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.

• percentage

A percentage is a rate per 100.

For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.