Unit Rates
Constant of Proportionality
Using Proportions to Solve for Unknown
100
A scale drawing of a rectangular rug has the dimensions 4.25 cm and 2.5 cm. The scale of the actual rug to the drawing is 4 ft to 1 cm. What is the actual area of the rug?

170 ft2

100

Identify the Constant of Proportionality in the equation g=9f

9

100

Kara can read 30 pages in one hour. How many hours will it take her to read 120 pages?

4 hours

200

Mark bought an 18 ounce smoothie that contained 225 calories. How many calories does the smoothie contain per ounce?

12.5 calories per ounce

200

2 t-shirts costs $20. What is the constant of proportionality for that ratio?

10

200

The ratio of cups of sugar used cups of chocolate chips used in a recipe is 2 to 1.5. If Kyle uses 8 cups of sugar how many cups of chocolate chips should he use?

6 cups of chocolate chips

300

Bob and his wife went on a trip to the beach. They traveled 130 miles and it took them 3 hours. The couple stopped for a half hour for a snack. What was their average rate of speed without stopping for a snack?

52 miles per hour 

300

A farm stand sells oranges in 6 lb bags. Each bag costs $7.50. Write an equation that represents the cost, c, for p  pounds of oranges?

c=1.25p or p=c/1.25

300

In a recipe, for every 1/3 cup of sugar, 3/4 cup flour is needed. How many cups of sugar are needed for 2 cups of flour? 

8/9 cup of sugar

400

Mary traveled 125 miles in 2.5 hours. Will traveled 141 miles in 3 hours. Who is faster? How much faster?

3 miles per hour; Mary

400

Julia types at a constant rate of 42 words per minute. Write an equation to show the relationship between the number of words she types, w, and the number of minute she types, m. 

w=42m or m=w/42

400

The distance on a map between Lake Village and Bay Cove is 2.25 inches. If 1 inch represents 15 miles, what is the actual distance between Lake Village and Bay Cove?

33.75 miles

500
A rectangular playground is drawn to scale with the dimensions 6 cm by 4 cm. The scale from the playground to this drawing is 5 ft to 1 cm. Another drawing was made with the scale 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?

3.75 cm and 2.5 cm

500

Explain what it means to spend 2 hours painting with 3 paintings completed and 4 hours painting with 6 paintings completed using the vocab terms proportion and/or unit rate. 

There is a proportional relationship between the number of hours spent painting and the number of paintings completed. The constant of proportionality, or the unit rate, is 2/3. This means it takes 2/3 hr to complete 1 painting. 

500

Maxwell wants to project a movie from his phone to the screen on the wall. The side length of the screen is 56 in. The scale from the screen to the phone is 8 in to 1 in. What is the side length of Maxwell's phone?

7 in

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