Proportional Relationships
Debra can run 20 1/2 miles in 2 1/4 hours. How many miles per hour can she run?
What is 9 1/9 miles per hour?
Solution: miles ÷ hour
20 1/2 ÷ 2 1/4= 9 1/9
Last week Dino spent $18.00 to bowl 4 games. This week he spent $27.00 to bowl 6 games. Dino owns his bowling ball and shoes, so he only has to pay for each game that he bowls. If each of these bowling games cost the same amount of money, what is the constant of proportionality between the money spent and the number of games played?
What is 4.5 ?
Solution:
18 ÷ 4=4.5
OR 27 ÷ 6=4.5
The table below shows the distance that a train traveled over 7.5 hours.
What is the speed that the train is traveling per hour?
What is 40 miles per hour?
Solution: Y ÷ X (Miles ÷ Hour)
The graph below shows the cost of wall tiles. Based on the graph, what is the cost per tile?
What is $1.50 ?
Solution: Y ÷ X (Cost ÷ Tiles)
$6 ÷ 4= $1.50
$12 ÷ 8 = $1.50
$18 ÷ 12= $1.50
Bananas cost $0.45 per pound. What equation is used to find C, the total cost of p pounds of bananas?
What is c = 0.45p ?
A recipe for rice pudding calls for 2 1/2 cups of milk. The recipe makes 5 servings. How many cups of milk are needed to make 8 servings?
What is 4 cups?
Solution:
2 1/2/5 = N/8
A crew of highway workers paved 2/15 mile in 20 minutes. If they continue to work at the same rate, what portion of a mile will they pave in one hour?
What is 2/5 ?
Solution: mile ÷ time
2/15 ÷ 20/60= 2/5
Symone is running a marathon. The table shows how far she has run. What equation relates the distance Symone has run, d, to the time in hours, t?
What is d=7.5t ?
The graph below represents the cost for peanuts at a local supermarket. What is the constant of proportionality from the graph?
What is 3.5?
Solution: Y divided by X
(2, 7) (3, 10.5) (4, 14) (5, 17.5)
The cost of oranges in a grocery store is directly proportional to the number of oranges purchased. Jerri paid $2.52 for 6 oranges. If p represents the cost, in dollars, and n represents the number of oranges purchased, which equation best represents this relationship?
What is P= 0.42n ?
Solution:
$2.52 ÷ 6= .42
The label on a 11/2 – pound bag of wildflower seeds states that it will cover an area of 375 square feet. Based on this information, what is the number of square feet that 2 3/4 pounds of wildflower seeds will cover?
What is 687.5 ft2 ?
Ms. Richards gave her class 12 minutes to read. Alex read 5 1/2 pages in that time. At this rate, how many pages will Alex read per hour?
What is 27.5 pages?
Solution: Pages ÷ Time
5 1/2 ÷ 12= 11/24 (pages per minute)
11/24 x 60= 27 1/2 or 27.5
OR 5 1/2 ÷ 12/60=27 1/2 or 27.5
What is the constant of proportionality for the following table?
What is 15 ?
Solution: Y divided by X
30/2 , 60/4, 90/6, 120/8
Based on the graph below, who, if any, of the participants pass levels at a constant rate?
Who is Morgan ?
Solution: Morgan is a straight line that passes through the origin.
The scale on floor plan is 1 in.: 8 ft. What actual distance does a distance of 2.6 inches on the floor plan represent?
What is 20.8 ft ?
Solution: Inches x Feet
2.6 x 8
A car dealership sold 44 cars this month. For every 4 red cars sold, 7 blue cars are sold. How many of the cars sold this month were blue?
What is 28 blue cars?
Solution: 44 represents the total number of cars so add 4 + 7 to find the total number of cars in the original ratio.
7/11 = N/44
Mr. Warnock drove 96 miles in 11/2 hours. What was his speed in miles per hour?
What is 64 miles per hour?
Solution: miles ÷ hour
96 ÷ 1 1/2= 64
Tell whether the data sets show a proportional relationship. If so, identify the constant of proportionality.
What is Proportional, K=4?
Solution: Y divided by X
The graph below shows the relationship between the number of people in a group and the total cost of admission tickets for a circus. What point on the graph represents the unit rate?
What is (1, 15)?
Solution: Unit rate is always represented by (1, R)
A high-speed elevator can rise 480 feet in 30 seconds. Which expression represents the rate, in feet per minute, of the elevator?
What is 480(2)?
Solution: 30 seconds is half a minute so multiply by 2 to find how many feet in one minute.
Matthew worked 8.5 hours and earned $102.00. At that rate, how much will Matthew earn after working for 19 hours?
What is $228?
Francesca typed 496 words in 8 minutes. How many words can she type per minute?
What is 62 words per minute?
Solution: Words ÷ minute
496 ÷ 8= 62
Jerome went on a hike. He climbed three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles per hour?
What is 1 1/8 miles per hour?
Solution: 3/4 divided by 2/3
A recycling plant processes an average of 1/3 ton of glass each minute. At approximately what rate does the recycling plant process glass, in tons per day?
What is 480 ?
Solution:
1/3 x 60= 20 tons
20 x 24=480 tons per day
A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water are needed for each cup of milk?
What is 3/4 cups of water?
Solution: Water divided by milk
1/4 divided by 1/3