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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?

Respuesta :

frika

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,

[tex]a_1=\$68\\ \\a_2=\$65\\ \\a_3=\$62\\ \\...[/tex]

where [tex]a_n[/tex] is the rate per nth room rented.

This is an arithmetic sequence, so

[tex]a_n=a_1+(n-1)\cdot d[/tex]

In your case,

[tex]a_1=68\\ \\n=10\\ \\d=-3[/tex]

Hence

[tex]a_{10}=68+(10-1)\cdot (-3)=68-9\cdot 3=68-27=41[/tex]

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

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