Unit Rates
The table below shows the relationship between the number of tickets sold and the total cost. What is the unit rate in dollars per ticket?
Tickets Cost ($)
3 15
5 25
8 40
$5 per ticket
Identify the constant of proportionality, k, in the equation y = 12x
k = 12
A map uses a scale of 1 inch = 5 feet. If the distance between two trees on the map is 4 inches, what is the actual distance between the trees?
Identify the name for each part.
A - A line segment that connects the center to any point on the edge.
B - A line segment that passes through the center and connects two points on the edge.
C - A line segment that connects two points on the edge but does not pass through the center.
D - The specific point in the exact middle of the circle.
A - Radius
B - Diameter
C - Chord
D - Center
A recipe for blueberry muffins uses 6 cups of blueberries for every 3/4 cup of flour. If you want to use 3 cups of flour to make a larger batch, how many cups of blueberries will you need?
24 cups of blueberries
For every 1/4 mile that a turtle crawls, it takes 1/8 hour. What is the turtle's unit rate in miles per hour?
2 miles per hour
A grocery store sells 8 pounds of organic apples for $20. Write an equation that represents the relationship between the total cost, c, and the weight in pounds, w.
c = 2.5w
A designer is creating a scale drawing of a rectangular room that is 32 feet long and 24 feet wide. The scale is 1 inch : 8 feet. What are the dimensions of the room in the drawing?
4 inches by 3 inches
A circular mirror has a diameter of 12 inches. What is the circumference of the mirror? (Use 3.14 for π).
C = 37.68 inches
A recipe for a cleaning solution calls for 1/2 cup of vinegar, 1/8 cup of dish soap, and 2 3/8 cups of water. How much dish soap is needed to make a total of 12 cups of this cleaning solution?
1/2 cup or 0.5 cup
What is the unit rate of the ratio 3/5 : 9/10?
The unit rate is 2/3
A concrete mixture uses 12 cups of gravel for every 3/4 cup of cement. What is the constant of proportionality for the relationship of cups of gravel to cups of cement?
16 cups of gravel per cup of cement
Emma has a square photo with a side length of 5 inches. She enlarges it to fit a square canvas with an area of 25 square feet. What is the scale from the original photo to the canvas?
1 inch to 1 foot
A circular rug has a diameter of 16 feet. What is the area of the rug? Write your answer in terms of π.
A = 64π
A plumber charges a flat fee of $50 for a service call plus $75 per hour of work. If a customer is charged a total of $275, how many hours did the plumber work?
3 hours
A graph of a proportional relationship passes through the origin (0,0) and the point (4,18), where x represents pounds and y represents total cost. What is the unit rate in dollars per pound?
$4.50 per pound
Use the table below to write an equation in the form c = kd that relates the total cost, c, to the number of days, d, for an equipment rental.
Days (d) Cost (c)
3 $45
5 $75
8 $120
c = 15d
A large container holds 15 gallons of water. Use the conversion factor 1 gal = 3.8 L to find how many liters of water are in the container.
57 liters of water
A bicycle wheel has a diameter of 14 inches. How many inches will the bicycle travel after the wheel completes 20 full rotations? (Use 3.14 for π).
The bike travels 879.2 inches.
Mr. Oliveros buys theater tickets for himself and his students. He spends $45 in total. He spends $10 for his own adult ticket and spends the rest on student tickets. If each student ticket costs $2.50, how many students is he taking to the play?
14 students
Brand A sells a 12-ounce box of cereal for $3.60. Brand B sells an 18-ounce box of the same cereal for $4.50. Which brand has the lower unit rate, and by how much per ounce?
Brand B has lower by $0.05 per ounce
Brand A: $0.30 per ounce
Brand B: $0.25 per ounce
A scientist mixes a solution using 2/5 gram of salt for every 10 mL of water. Write an equation that relates the number of mL of water, w, to the number of grams of salt, s .
w = 25 s
A square garden has a side length of 4 yards. A scale drawing of the garden uses a scale of 1 inch : 2 yards.
Part A: What is the area of the actual garden in square yards?
Part B: What is the area of the garden in the scale drawing in square inches?
Part A: 16 sq yards
Part B: 4 sq inches
The circumference of a circular fountain is 31.4 feet. What is the radius of the fountain? (Use 3.14 for π).
Radius = 5 feet
A designer is planning a square outdoor deck. On the scale drawing, the side length of the deck is 5 inches. The actual deck will have a total area of 400 square feet.
Part A: What is the scale from the drawing to the actual deck (1 inch to how many feet)?
Part B: If the wood for the deck costs $8.50 per square foot, what is the total cost of the materials for the deck?
Part A: 1 inch to 4 feet
Part B: $3,400