# Lesson 11Percentages and Double Number Lines

Let’s use double number lines to represent percentages.

### Learning Targets:

• I can use double number line diagrams to solve different problems like “What is 40% of 60?” or “60 is 40% of what number?”

## 11.1Fundraising 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. 1. Lin raised 100% of her goal. 2. Jada raised 50% of her goal. 3. Andre raised 150% of his goal. ## 11.2Three-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? ## 11.3Puppies 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? ### Are you ready for more? A loaf of bread costs$3.00 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? ## Lesson 11 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 the distance between 0 and 50 pounds into ten equal parts. We label the tick marks on the top line by counting by 5s () and on the bottom line counting by 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.

## Lesson 11 Practice Problems

1. Solve each problem. If you get stuck, consider using the double number lines.

1. During a basketball practice, Mai attempted 40 free throws and was successful on 25% of them. How many successful free throws did she make?

2. Yesterday, Priya successfully made 12 free throws. Today, she made 150% as many. How many successful free throws did Priya make today?

2. A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?

3. At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If 100 sixth-grade students prefer hip hop music, how many sixth-grade students are at the school? Explain or show your reasoning.
4. Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can along a straight, level path.

vehicle distance traveled
skateboard 90 feet
scooter 1,020 inches
bike 4,800 centimeters
go-cart 0.03 kilometers
1. 100 inches equal 254 centimeters. What is the distance each vehicle traveled in centimeters?
2. Rank the vehicles in order from fastest to slowest.
5. It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:

1. How many pounds of mashed potatoes can they make with 15 pounds of potatoes?
1. How many pounds of potatoes are needed to make 50 pounds of mashed potatoes?