Lesson 11
Percentages and Double Number Lines
Let’s use double number lines to represent percentages.
11.1: Fundraising Goal
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.

Lin raised 100% of her goal.

Jada raised 50% of her goal.

Andre raised 150% of his goal.
11.2: ThreeDay Biking Trip
Elena biked 8 miles on Saturday. Use the double number line to answer the questions. Be prepared to explain your reasoning.

What is 100% of her Saturday distance?

On Sunday, she biked 75% of her Saturday distance. How far was that?

On Monday, she biked 125% of her Saturday distance. How far was that?
11.3: Puppies Grow Up

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?

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?
 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.
 What percentage of today’s price did someone in 1955 pay for bread?
 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%.