Question

Leticia recently rented an office space and now needs someone to do weekly cleaning. She received these bids from two different cleaning services.

Quick Clean charges a $30 cleaning supply fee for every visit and $20 per hour.
Three Friends Cleaners provided the table below to show its cost.




Hours Cleaning Cost
0.5 $12.50
1.0 $25.00
1.5 $37.50
2.0 $50.00
... ...
20.0 $500.00




Which statement comparing the costs of the two cleaners is true?


If it takes 5 hours for Leticia's office space to be cleaned, Three Friends Cleaners is less expensive than Quick Clean.


If it takes 10 hours for Leticia's office space to be cleaned, Three Friends Cleaners is less expensive than Quick Clean.


If the cleaning costs for each company were graphed, the y-intercepts would be the same.


Three Friends Cleaners charges $5 less per hour than Quick Clean.

Answer 1

Quick Clean: C_Q(h) = 30 + 20h.
Three Friends: C_T(h) = 25h.

For 5 hours: C_T(5) = 125, C_Q(5) = 130 → Three Friends is less expensive. (True)

The other statements are false:
- For 10 hours: C_T(10)=250, C_Q(10)=230 → Three Friends is more expensive. (False)
- y-intercepts: C_Q(0)=30 vs C_T(0)=0, not the same. (False)
- Hourly rates: Three Friends charges $25/hr, Quick Clean $20/hr, so Three Friends charges $5 MORE per hour, not less. (False)