Question

101 which of the following describes a proportional relationship? Select all that apply.

a. Nathalie works as a private fitness trainer and earns $40 per person she trains.
b. Luis is a waiter and earns $6 an hour plus tips.
c. Jonathan works at Subway and makes $8.26 per hour.
d. Jackie is a computer tech and charges $15 for a house visit plus $20 an hour.
e. Jayden saved $10 his first month and $50 the next 5 months.
Maria spent $5 in 5 days and $10 the next 8 days.
Robert saved $4 in the first 2 days and $15 the next 6 days.
h. Alyssa pays $2 to rent a movie each day.
i.
Corey pays $2 to rent a movie on the first day and $1 for each day after that.
]. Perla pays a $5 monthly membership fee in addition to $2 a day for a renting a movie.

Answer 1

All of these relationships show a direct proportionality between two quantities. The other scenarios mentioned do not exhibit proportional relationships.

Explanation:

A proportional relationship exists when one quantity is a constant multiple of another. In this case, we are looking for relationships where the amount earned or saved is directly proportional to some input (e.g., time worked or the number of people trained). Here are the relationships that describe a proportional relationship:

a. Nathalie works as a private fitness trainer and earns $40 per person she trains.

- This is a proportional relationship because the earnings are directly proportional to the number of people trained.

c. Jonathan works at Subway and makes $8.26 per hour.

- This is a proportional relationship because earnings are directly proportional to the number of hours worked.

e. Jayden saved $10 his first month and $50 the next 5 months.

- This is a proportional relationship because the amount saved is directly proportional to the number of months.

i. Corey pays $2 to rent a movie on the first day and $1 for each day after that.

- This is a proportional relationship because the cost of renting a movie is directly proportional to the number of days rented.

]. Perla pays a $5 monthly membership fee in addition to $2 a day for renting a movie.

- This is a proportional relationship because the cost of renting a movie is directly proportional to the number of days rented, with the addition of a fixed monthly fee.

The relationships that are not proportional are:

b. Luis is a waiter and earns $6 an hour plus tips.

- Earnings are not directly proportional to the number of hours worked since tips can vary significantly.

d. Jackie is a computer tech and charges $15 for a house visit plus $20 an hour.

- The cost is not directly proportional to the number of hours since there's a fixed fee for the house visit.

h. Alyssa pays $2 to rent a movie each day.

- This is not proportional because the cost is a fixed $2 per day and does not depend on the number of days rented.

The remaining scenarios (Maria's and Robert's) are savings patterns and do not represent proportional relationships since the amounts saved are not directly proportional to the time periods involved.