SOLUTION: A banquet hall charges a rental fee plus an additional charge for each guest. The total cost is $550 for 20 guests and $775 for 35 guests. Find an equation to model the total cos

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A banquet hall charges a rental fee plus an additional charge for each guest. The total cost is $550 for 20 guests and $775 for 35 guests. Find an equation to model the total cos      Log On


   

Question 1187922: A banquet hall charges a rental fee plus an additional charge for each guest. The total cost is $550 for 20 guests and $775 for 35 guests.
Find an equation to model the total cost, C, in terms of the number of guests, N.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Informally....

The additional 35-20=15 guests cost an additional $775-$550=$225, so the cost per guest is $225/15 = $15.

Since the cost for 20 guests is $550, the rental fee is $550-20($15)=$550-$300=$250.

So the rental cost is a fee of $250 plus $15 per guest.

Using formal algebra -- note that the calculations performed are exactly the same....

(x(1),y(1))=(20,550)
(x(2),y(2))=(35,775)

The slope m (increase in cost (y) per guest (x)) is



The equation is of the form y=mx%2Bb; and we know the slope m is 15. Plug in (x,y) = (20,550) to find b.

550+=+15%2820%29%2Bb
550+=+300%2Bb
b=250

ANSWER: The equation for the total cost C for N guests is

C=15N%2B250