Complex algebra question?

Question

You're in the hotel business. You own one hotel, from which you earn $100/hr. Your goal is to own ten hotels in total. Hotels cost $5,000, but for each one you own, the seller raises the price of hotels by $1,000 (so currently, they cost $6,000). At any time, you can sell back for the current cost/2. What is the fastest way to own ten hotels?

Answer 1

wow tough question. there would be no point in selling one back so that part is irrelavent.

basically in the start you have one. the 2nd costs $6000, 3rd costs $7000... 10th costs $14 000

you want to buy another ASAP so as soon as you have $6000 you want to buy the 2nd so you earn money twice as fast.

so the length of time it will take to buy a new hotel is:

cost of hotel/(100*# of hotels owned)

and cost of hotel is just ($1000*#of hotels owned + $4000)

so let n be # of hotels owned and t be time it takes to buy the new hotel (in hours) your equation is

t = (1000n+5000)/(100n)

t = (50/n) + 10

But you must apply this to every integral value of n from 1-9 (when 9 are owned you will be purchasing the 10th) and add them together

so

n=1 t=60

n=2 t=35

n=3 t=80/3

n=4 t=45/2

n=5 t=20

n=6 t=55/3

n=7 t=120/7

n=8 t=65/4

n=9 t=140/9

so adding all the t values together we get 231.45 hours or 9.64 days