Understanding Proportional Relationships Quiz

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Questions and Answers

What amount of hay consumed in pounds should be input for 7 days to keep the table proportional?

6 (correct)

Which equation correctly represents the relationship between the amount of hay, h, and days, d?

h = d

h = 30d

h = 2d

h = 15d (correct)

Which of the following relationships has a constant of proportionality equal to 14?

p = 14h

y = 14x (correct)

y = x + 14

p = 14d

If Paola paid $125 for 5 days of dog daycare, how much does she pay per day?

$25 Signup and view all the answers

Which equation models the amount Paola pays, p, in dollars for her dog to attend dog daycare for d days?

p = 25d Signup and view all the answers

In the context of the coffee shop, if 4 hours worked results in a pay of $56, what is the constant of proportionality?

14 Signup and view all the answers

How many workbooks does the copy machine print in 6 minutes if it prints 30 workbooks every 2 minutes?

90 Signup and view all the answers

Regena's walking speed is constant. What distance has she walked if it took her 42 minutes to walk 3 miles?

3 miles Signup and view all the answers

What is the cost per book if 2 books are purchased for $8?

$4 Signup and view all the answers

Which equation correctly represents the relationship between the number of minutes, m, and pages printed, p, for the copy machine?

p = 42m Signup and view all the answers

How much hay would be consumed by each horse over 7 days, based on the provided data?

105 pounds Signup and view all the answers

If the cost of buying 4 books is $16, what can be inferred about the relationship between the number of books purchased and total cost?

The cost is directly proportional to the number of books. Signup and view all the answers

In how many minutes does the copy machine print 336 pages?

8 minutes Signup and view all the answers

What is the total amount of hay consumed after 4 days according to the table?

60 pounds Signup and view all the answers

What is the proportionality constant for the number of pages printed per minute based on the given data?

42 pages per minute Signup and view all the answers

Which of the following statements is true regarding the hay consumed over the observed days?

The relationship shows a constant increase of hay per day. Signup and view all the answers

What is the length, in inches, of Print B?

36 Signup and view all the answers

What is the scale factor from figure A to figure B?

4 Signup and view all the answers

How many total servings does Akio make when using 5 cups of lemon juice?

17.5 Signup and view all the answers

Why does Akio’s table represent a proportional relationship?

The ratio of cups of lemon juice to total servings is constant. Signup and view all the answers

Which of the following statements about Beth's lemonade recipe is true?

The lemon juice amount does not lead to consistent servings. Signup and view all the answers

If Akio makes 10 cups of lemon juice, how many servings does he produce?

35 Signup and view all the answers

What is the constant of proportionality in Akio’s lemonade recipe?

3.5 Signup and view all the answers

What happens to the total servings when more lemon juice is added in Beth’s recipe?

Servings increase but not proportionally. Signup and view all the answers

Which table demonstrates a proportional relationship between $x$ and $y$?

Table 2: ${(3, 6), (6, 12), (9, 18), (12, 24)}$ Signup and view all the answers

What is the equation that represents the amount in dollars, $c$, that Tram charges to babysit $h$ hours if she charges a constant rate?

$c = 16h$ Signup and view all the answers

Is the number of minutes that Naveen biked proportional to the distance, in miles, that he biked?

No, because the time increases more than linearly with distance. Signup and view all the answers

If Tram charges $16 per hour to babysit, how much would she charge for 5 hours?

$80 Signup and view all the answers

In the context of Naveen's bike ride, what is the time taken per mile for the first two data points (2 miles in 22 minutes and 5 miles in 50 minutes)?

10 minutes per mile Signup and view all the answers

What is the origin point in the context of a proportional relationship?

(0, 0) Signup and view all the answers

If Naveen biked 12 miles in 138 minutes, what is the average speed in miles per minute?

0.09 miles/min Signup and view all the answers

Which of the following statements is true regarding a proportional relationship?

It must consist of pairs of numbers that maintain a constant ratio. Signup and view all the answers

What is the area of the actual park in square meters if the scale drawing is 18 cm by 12 cm and the actual width is 108 meters?

1,944 Signup and view all the answers

What is the unit rate of water filling a fish tank if it takes 20 minutes to fill with 30 gallons?

2 Signup and view all the answers

What is the actual distance in feet from the park entrance to the roller coaster if the map scale states that 3 cm equals 60 feet and the distance on the map is 22 cm?

440 Signup and view all the answers

What is the cost per pound of honeycrisp apples if 3 pounds cost $7.47?

2.49 Signup and view all the answers

What will be the length of Print A if it is a scaled copy of the original print of 72 inches using a scale factor of 3?

144 Signup and view all the answers

What size will Print B be in width if it scales Print A's width of 54 inches using a scale factor of 4?

288 Signup and view all the answers

If the total cost of 5 pounds of honeycrisp apples is $12.45, what would be the total cost for 10 pounds at the same rate?

24.90 Signup and view all the answers

If Serina's tank filled at a unit rate of 1.5 gallons per minute, how long in minutes would it take to fill 45 gallons?

30 Signup and view all the answers

Study Notes

Used Bookstore Book Costs

The cost of books at a used bookstore is proportional to the number of books purchased.
The cost per book is $4.

Copy Machine Printing Rate

A copy machine prints at a constant rate.
The equation representing the number of pages (p) printed in m minutes is p = 42m.

Hay Consumption by Horses

The amount of hay consumed by each horse is proportional to the number of days.
Over 7 days, each horse consumes 105 pounds of hay.
The equation representing the amount of hay (h) consumed over d days is h = 15d.

Proportional Relationships

A table showing a proportional relationship between x and y is:
- x | y
- 3 | 6
- 6 | 12
- 9 | 18
- 12 | 24

Babysitting Charges

Tram charges a constant rate per hour for babysitting.
When she babysits 8 hours, she charges $128.
The equation representing the amount (c) charged for h hours is c = 16h.

Naveen's Bike Ride

The relationship between the number of minutes Naveen biked and the distance is not proportional.

Additional Proportional Relationships Problems

The constant of proportionality for the relationship y = 14x is 14.
The cost of theater tickets is proportional (constant of proportionality is 12.5).
The coffee shop pay is proportional (constant of proportionality is 14).
Regena’s walking rate is 14 minutes per mile (not 14).
The printing rate of the copy machine is 15 workbooks per minute ( not 14).
Paola pays $25 per day for doggie daycare; the equation is p = 25d.

Scale Drawing of a Park

Minh’s scale drawing of a park is 18 cm long and 12 cm wide.
The actual park is 108 meters wide.
The area of the actual park is 17,496 square meters.

Fish Tank Filling Rate

A fish tank is filled at a constant rate.
It takes 20 minutes to fill the tank with 30 gallons of water.
The unit rate is 1.5 gallons per minute.

Distance from Park Entrance to Roller Coaster

A map has a scale of 3 cm representing 60 feet.
The distance on the map is 22 cm.
The actual distance is 440 feet.

Cost of Honeycrisp Apples

The cost of honeycrisp apples is proportional to the number of pounds purchased.
The cost per pound is $2.49.

Photographer's Prints

The original print has dimensions 72 inches by 54 inches.
Print A is a scaled copy with a scale factor of 2/3.
Print B is a scaled copy of Print A with a scale factor of 4/3.
The length of Print B is 64 inches. This is incorrect 72 * (2/3) * (4/3) = 192

Scale Factor of Figures

Figure B is a scaled copy of Figure A.
The scale factor from Figure A to Figure B is 1/4.

Akio and Beth's Lemonade Recipes

Akio's lemonade recipe shows a proportional relationship between servings and cups of lemon juice.
Beth's lemonade recipe does not show a proportional relationship.
Akio's constant of proportionality is 3.5.

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Description

This quiz explores various real-world applications of proportional relationships, including pricing for books, printing rates, hay consumption, and babysitting charges. Test your understanding of how to formulate equations representing these proportional scenarios.