Solving systems of equations word problems - classwork

1. to rent scooters, sam's scooters charges a $30 fee plus $8 per hour. rosie's charges a $20 fee
plus $10 per hour.

independent variable (x):

dependent variable (y):

system of equations:

points on the graph:

questions.

a. when does it make more sense to rent a scooter from rosie's? how do you know?

b. when does it make more sense to rent a scooter from sam's? how do you know?

c. is there ever a time where it wouldn't matter which store to choose? explain.

d. if you were renting a scooter from rosie's, how much would you pay if you were planning on renting for 7 hours? show your work.

Part A) For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's

Part B) For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's

Part C) Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters

Part D) The cost is $90

Step-by-step explanation:

Let

x-------> the number of hours (independent variable)

y-----> the total cost of rent scooters (dependent variable)

we know that

Sam's scooters

Rosie's scooters

using a graphing tool

see the attached figure

A. when does it make more sense to rent a scooter from Rosie's? How do you know?

For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's  (see the attached figure) because the cost in less than Sam' scooters

B. when does it make more sense to rent a scooter from Sam's? How do you know?

For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's  (see the attached figure) because the cost in less than Rosie' scooters

C. Is there ever a time where it wouldn't matter which store to choose?

Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters. The cost is $70 (see the graph)

D. If you were renting a scooter from Rosie's, how much would you pay if you were planning on renting for 7 hours?

Rosie's scooters

For x=7 hours

substitute

The cost is $90