Math Is Fun Forum

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Tricky wording

The owner of a 20 room motel must take in $66000 a year to cover costs and earn a reasonable profit.

a) If the average occupancy level is 70% and the same daily rate is charged for all occupied rooms, what should this rate be (to the nearest dollar)?

≈ $13

b) If the owner decides to charge $3 more than the single occupancy rate if two or more people occupy the room, what should the two rates be (given that on average, two or more people are in 75% of the occupied rooms)?

Well, I've just figured out what the two rates would be: The single occupancy rate and the two or more occupancy rate, but the answers couldn't be as simple as $13 and $16...
Are only 75% of the rooms occupied? What about the other 25%? Singularly occupied? Not at all? I give this question a

Last edited by Toast (2006-12-04 22:44:38)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Tricky wording

a) is a flat rate per room
b) is a different rate based on whether 1 or 2-or-more people occupy a room (and I assume all other conditions are the same such as occupancy rate)

So, 75% of occupied rooms have 2+ people, and 25% have one

And we want to achieve the $13 you calc'd in a)

Call the two rates "s" and "d"

0.25s + 0.75d = 13
d - s = 3

I get s = 10.75 and d = 13.75

Does that seem right?

---

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Tricky wording

Thanks MathsIsFun, I solved those and got
d = 13.75 and s = 10.75.
However, the answers suggest 14 and 11 respectively.
I'm not ruling out the answers are wrong (as they often are), and the working seems right, but... meh, answers guilty until proven innocent.

EDIT #2: (I did 13*24 instead of 13*20 [gaaaaarh!], so now that it stands corrected my equation and yours both give the same results, so I have little doubt that we are both right )

PREVIOUS EDIT (IGNORE if u want)
BTW, I previously had in mind,
d-s=3
5s+15d=13*20
Where the first equation is obvious and the second equation represents daily income for the respective 25% and 75% of rooms.
To me it also looks right, but does not yield the same solution, why?

Last edited by Toast (2006-12-04 23:01:16)