Question

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

One room rents for $68, two rooms for $65 each and in general the group rate per room is
found by taking $3 off the base of $68 for each extra room. How much money do you
charge per room if a group rents 10 rooms?

Answer 1

$41

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.