Question

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.
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Answer 1

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

Explanation:

Let

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

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

we know that

Sam's scooters

`y=8x+30`

Rosie's scooters

`y=10x+20`

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

`y=10x+20`

For x=7 hours

substitute

`y=10(7)+20=90`

The cost is $90