Unit 3: Practice Problem Sets

An elevator travels 310 feet in 10 seconds. At that speed, how far can this elevator travel in 12 seconds? Explain your reasoning.

Han earns \$33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 7 hours? Explain your reasoning.

The cost of 5 cans of dog food is \$4.35. At this price, how much do 11 cans of dog food cost? Explain your reasoning.

A restaurant has 26 tables in its dining room. It takes the waitstaff 10 minutes to clear and set 4 tables. At this rate, how long will it take the waitstaff to clear and set all the tables in the dining room? Explain or show your reasoning.

A sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich. After making sandwiches for an hour, the shop owner has used 91 combined ounces of meat and cheese.

1. How many combined ounces of meat and cheese are used on each sandwich?
2. How many sandwiches were made in the hour?
3. How many ounces of meat were used?
4. How many ounces of cheese were used?

Here is a flower made up of yellow hexagons, red trapezoids, and green triangles.

1. How many copies of this flower pattern could you build if you had 30 yellow hexagons, 50 red trapezoids, and 60 green triangles?
2. Of which shape would you have the most left over?

Select the unit from the list that you would use to measure each object.

When this pet hamster is placed on a digital scale, the scale reads 1.5.

Circle the larger unit of measure. Then, determine if the unit measures distance, volume, or weight (mass).

Elena mixes 5 cups of apple juice with 2 cups of sparkling water to make sparkling apple juice. For a party, she wants to make 35 cups of sparkling apple juice. How much of each ingredient should Elena use? Explain or show your reasoning.

Lin bought 3 hats for \$22.50. At this rate, how many hats could she buy with \$60.00? If you get stuck, try using the table. 

Light travels about 180 million kilometers in 10 minutes. How far does it travel in 1 minute? How far does it travel in 1 second? Show your reasoning.

Decide if each is a measurement of length, area, volume, or weight (or mass).

1. How many centimeters across a handprint
2. How many square inches of paper needed to wrap a box
3. How many gallons of water in a fish tank
4. How many pounds in a bag of potatoes
5. How many feet across a swimming pool
6. How many ounces in a bag of grapes
7. How many liters in a punch bowl
8. How many square feet of grass in a lawn

Clare says, “This classroom is 11 meters long. A meter is longer than a yard, so if I measure the length of this classroom in yards, I will get less than 11 yards.” Do you agree with Clare? Explain your reasoning.

Noah bought 15 baseball cards for \$9.00. Assuming each baseball card costs the same amount, answer the following questions.

1. At this rate, how much will 30 baseball cards cost? Explain your reasoning.
2. At this rate, how much will 12 baseball cards cost? Explain your reasoning.
3. Do you think this information would be better represented using a table or a double number line? Explain your reasoning.

Jada traveled 135 miles in 3 hours. Andre traveled 228 miles in 6 hours. Both Jada and Andre traveled at a constant speed.

1. How far did Jada travel in 1 hour?
2. How far did Andre travel in 1 hour?
3. Who traveled faster? Explain or show your reasoning.

Priya’s family exchanged 250 dollars for 4,250 pesos. Priya bought a sweater for 510 pesos. How many dollars did the sweater cost?

There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. For each question, explain or show your reasoning.

1. How many milliliters are in 3 gallons?
2. How many milliliters are in 1 quart?

Tyler has a baseball bat that weighs 28 ounces. Find this weight in kilograms and in grams. (Note: 1 kilogram $\approx$ 35 ounces)

Identify whether each unit measures length, volume, or weight (or mass).

A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. (Almonds and raisins are the only ingredients.) How many ounces of almonds would be in a one-pound bag of this trail mix? Explain or show your reasoning.

An ant can travel at a constant speed of 980 inches every 5 minutes.

1. How far does the ant travel in 1 minute?
2. At this rate, how far can the ant travel in 7 minutes?

Mai and Priya were on scooters. Mai traveled 15 meters in 6 seconds. Priya travels 22 meters in 10 seconds. Who was moving faster? Explain your reasoning.

Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal? Explain your reasoning.

Costs of homes can be very different in different parts of the United States.

1. A 450-square-foot apartment in New York City costs \$540,000. What is the price per square foot? Explain or show your reasoning.
2. A 2,100-square-foot home in Cheyenne, Wyoming, costs \$110 per square foot. How much does this home cost? Explain or show your reasoning.

There are 33.8 fluid ounces in a liter. There are 128 fluid ounces in a gallon. About how many liters are in a gallon?

1. 2
2. 3
3. 4
4. 5

Is your estimate larger or smaller than the actual number of liters in a gallon? Explain how you know.

Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? Explain your reasoning.

Name an object that could be about the same length as each measurement.

A pink paint mixture uses 4 cups of white paint for every 3 cups of red paint.

A farm lets you pick 3 pints of raspberries for \$12.00.

1. What is the cost per pint?
2. How many pints do you get per dollar?
3. At this rate, how many pints can you afford for \$20.00?
4. At this rate, how much will 8 pints of raspberries cost?

Han and Tyler are following a polenta recipe that uses 5 cups of water for every 2 cups of cornmeal.

• Han says, “I am using 3 cups of water. I will need $1\frac15$ cups of cornmeal.”
• Tyler says, “I am using 3 cups of cornmeal. I will need $7\frac12$ cups of water.”

Do you agree with either of them? Explain your reasoning.

A large art project requires enough paint to cover 1,750 square feet. Each gallon of paint can cover 350 square feet. Each square foot requires $\frac{1}{350}$ of a gallon of paint.

Andre thinks he should use the rate $\frac{1}{350}$ gallons of paint per square foot to find how much paint they need. Do you agree with Andre? Explain or show your reasoning.

Andre types 208 words in 4 minutes. Noah types 342 words in 6 minutes. Who types faster? Explain your reasoning.

A corn vendor at a farmer's market was selling a bag of 8 ears of corn for \$2.56. Another vendor was selling a bag of 12 for \$4.32. Which bag is the better deal? Explain or show your reasoning.

A car travels 55 miles per hour for 2 hours. Complete the table.

The table shows the amounts of onions and tomatoes in different-sized batches of a salsa recipe.

Complete the table so that the cost per banana remains the same.

Two planes travel at a constant speed. Plane A travels 2,800 miles in 5 hours. Plane B travels 3,885 miles in 7 hours. Which plane is faster? Explain your reasoning.

A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses $\frac{1}{35}$ of a gallon of gas to go 1 mile.

A box of cereal weighs 600 grams. How much is this weight in pounds? Explain or show your reasoning. (Note: 1 kilogram = 2.2 pounds)

A kangaroo hops 2 kilometers in 3 minutes. At this rate:

Mai runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4 laps of the track? Explain or show your reasoning.

At 10:00 a.m., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a pace of 15 minutes per mile.

1. How far does Han run after a half hour? After an hour?
2. Do Han and Tyler meet on the path within 1 hour? Explain or show your reasoning.

Two skateboarders start a race at the same time. Skateboarder A travels at a steady rate of 15 feet per second. Skateboarder B travels at a steady rate of 22 feet per second. After 4 minutes, how much farther will Skateboarder B have traveled? Explain your reasoning.

There are 4 tablespoons in $\frac14$ cup. There are 2 cups in 1 pint. How many tablespoons are there in 1 pint? If you get stuck, consider drawing a double number line or making a table.

Two larger cubes are made out of unit cubes. Cube A is 2 by 2 by 2. Cube B is 4 by 4 by 4. The side length of Cube B is twice that of Cube A.

1. Is the surface area of Cube B also twice that of Cube A? Explain or show your reasoning.
2. Is the volume of Cube B also twice that of Cube A? Explain or show your reasoning.

This package of sliced cheese costs \$2.97.

How much would a package with 18 slices cost at the same price per slice? Explain or show your reasoning.

A copy machine can print 480 copies every 4 minutes. For each question, explain or show your reasoning.

Order these objects from heaviest to lightest. (Note: 1 pound = 16 ounces, 1 kilogram $\approx$ 2.2 pounds, and 1 ton = 2,000 pounds)

Andre sometimes mows lawns on the weekend to make extra money. Two weeks ago, he mowed a neighbor’s lawn for $\frac{1}{2}$ hour and earned \$10. Last week, he mowed his uncle’s lawn for $\frac{3}{2}$ hours and earned \$30. This week, he mowed the lawn of a community center for 2 hours and earned \$30.

Which jobs paid better than others? Explain your reasoning.

Calculate and express your answer in decimal form.

1. Decompose this polygon so that its area can be calculated. All measurements are in centimeters.

2. Calculate its area. Organize your work so that it can be followed by others.

What percentage of a dollar is the value of each coin combination?

1. 4 dimes
2. 1 nickel and 3 pennies
3. 5 quarters and 1 dime

1. List three different combinations of coins, each with a value of 30% of a dollar.

2. List two different combinations of coins, each with a value of 140% of a dollar.

The United States government used to make coins of many different values. For each coin, state its worth as a percentage of \$1.

 

Complete the double number to line show percentages of \$50.

Elena bought 8 tokens for \$4.40. At this rate:

1. How many tokens could she buy with \$6.05?
2. How much do 19 tokens cost?

A snail travels 10 cm in 4 minutes. At this rate:

1. How long will it take the snail to travel 24 cm?
2. How far does the snail travel in 6 minutes?

1. 3 tacos cost \$18. Complete the table to show the cost of 4, 5, and 6 tacos at the same rate.

   	number of tacos	cost in dollars	rate in dollars per taco
   row 1	3	18
   row 2	4
   row 3	5
   row 4	6

   b. If you buy $t$ tacos for $c$ dollars, what is the unit rate?

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?

   

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?

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.

It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:

Here is a tape diagram that shows how far two students walked.

1. What percentage of Priya’s distance did Tyler walk?
2. What percentage of Tyler’s distance did Priya walk?

A bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients. Draw a tape diagram to show how many flavors have chocolate and how many don’t.

There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.

1. How many band members are sixth graders?
2. How many band members are seventh graders?
3. What percentage of the band members are eighth graders? Explain your reasoning.

Jada has a monthly budget for her cell phone bill. Last month she spent 120% of her budget, and the bill was \$60. What is Jada’s monthly budget? Explain or show your reasoning.

Which is a better deal, 5 tickets for \$12.50 or 8 tickets for \$20.16? Explain your reasoning.

An athlete runs 8 miles in 50 minutes on a treadmill. At this rate:

1. How long will it take the athlete to run 9 miles?
2. How far can the athlete run in 1 hour?

1. How can you find 50% of a number quickly in your head?

2. Andre lives 1.6 km from school. What is 50% of 1.6 km?

3. Diego lives $\frac 1 2$ mile from school. What is 50% of $\frac 1 2$ mile?

There is a 10% off sale on laptop computers. If someone saves \$35 on a laptop, what was its original cost? If you get stuck, consider using the table.

Explain how to calculate these mentally.

1. 15 is what percentage of 30?
2. 3 is what percentage of 12?
3. 6 is what percentage of 10?

Diego has 75% of \$10. Noah has 25% of \$30. Diego thinks he has more money than Noah, but Noah thinks they have an equal amount of money. Who is right? Explain your reasoning.

Lin and Andre start walking toward each other at the same time from opposite ends of 22-mile walking trail. Lin walks at a speed of 2.5 miles per hour. Andre walks at a speed of 3 miles per hour.

Here is a table showing the distances traveled and how far apart Lin and Andre were over time. Use the table to find how much time passes before they meet.

For each problem, explain or show your reasoning.

1. 160 is what percentage of 40?
2. 40 is 160% of what number?
3. What number is 40% of 160?

A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves \$13, what was the original price of her purchase? Explain or show your reasoning.

The original price of a scarf was \$16. During a store-closing sale, a shopper saved \$12 on the scarf. What percentage discount did she receive? Explain or show your reasoning.

An ant travels at a constant rate of 30 cm every 2 minutes.

1. At what pace does the ant travel per centimeter?
2. At what speed does the ant travel per minute?

Is 3$\frac{1}{2}$ cups more or less than 1 liter? Explain or show your reasoning. (Note: 1 cup $\approx$ 236.6 milliliters)

Name a unit of measurement that is about the same size as each object.

1. The distance of a doorknob from the floor is about 1 _____________.

2. The thickness of a fingernail is about 1 _____________.

3. The volume of a drop of honey is about 1 _____________.

4. The weight or mass of a pineapple is about 1 _____________.

5. The thickness of a picture book is about 1 _____________.

6. The weight or mass of a buffalo is about 1 _____________.

7. The volume of a flower vase is about 1 _____________.

8. The weight or mass of 20 staples is about 1 _____________.

9. The volume of a melon is about 1 _____________.

10. The length of a piece of printer paper is about 1 _____________.

1. To find 40% of 75, Priya calculates $\frac{2}{5} \boldcdot 75$. Does her calculation give the correct value for 40% of 75? Explain or show how you know.
2. If $x$ represents a number, does $\frac{2}{5} \boldcdot x$ always represent 40% of that number? Explain your reasoning.

Han spent 75 minutes practicing the piano over the weekend. For each question, explain or show your reasoning.

Order from greatest to least:

• 55% of 180
• 300% of 26
• 12% of 700

Complete each statement.

A shopper needs 24 sandwich rolls. The store sells identical rolls in 2 differently sized packages. They sell a six-pack for \$5.28 and a four-pack for \$3.40. Should the shopper buy 4 six-packs or 6 four-packs? Explain your reasoning.

On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the trip. Answer these questions. If you get stuck, consider using a tape diagram.

1. How many chaperones are there?
2. How many children are there?

A sign in front of a roller coaster says "You must be 40 inches tall to ride." What percentage of this height is:

1. 34 inches?
2. 54 inches?

At a hardware store, a tool set normally costs \$80. During a sale this week, the tool set costs \$12 less than usual. What percentage of the usual price is the savings? Explain or show your reasoning.

A bathtub can hold 80 gallons of water. The faucet flows at a rate of 4 gallons per minute. What percentage of the tub will be filled after 6 minutes?

The sale price of every item in a store is 85% of its usual price.

1. The usual price of a backpack is \$30, what is its sale price?
2. The usual price of a sweatshirt is \$18, what is its sale price?
3. The usual price of a soccer ball is \$24.80, what is its sale price?

A shopper needs 48 hot dogs. The store sells identical hot dogs in 2 differently sized packages. They sell a six-pack of hot dogs for \$2.10, and an eight-pack of hot dogs for \$3.12. Should the shopper buy 8 six-packs, or 6 eight-packs? Explain your reasoning.

Elena is 56 inches tall.

1. What is her height in centimeters? (Note: 100 inches = 254 centimeters)

2. What is her height in meters?