Question

You own a motel and have a pricing structure that encourages rentals of rooms in groups.

Answer 1

Answer:

$41

Step-by-step explanation:

• One room rents for $68,
• Two rooms for $65 each,
• In general, the group rate per room is found by taking $3 off the base of $68 for each extra room.

So,

$a_1=\ 68\\ \\a_2=\ 65\\ \\a_3=\ 62\\ \\...$

where $a_n$ is the rate per nth room rented.

This is an arithmetic sequence, so

$a_n=a_1+(n-1)\cdot d$

In your case,

$a_1=68\\ \\n=10\\ \\d=-3$

Hence

$a_{10}=68+(10-1)\cdot (-3)=68-9\cdot 3=68-27=41$

This means if a group rents 10 rooms, the charge per room is $41.