Monica is planning a party to be held at the local community hall. She is told by the hall manager that the cost, C, varies partially with the number of guests, n, that attend; that is, for each additional guest, the cost increases by the same amount.

People Cost

25 $70

50 $120

100 $220

Determine the equation of the variation in the form of C = mn + b. State any restrictions on n.

$\displaystyle C1 = 70 = 25m + b$

$\displaystyle C2 = 120 = 50m + b$

$\displaystyle 25m = 50 => m = 2 => b = 20$

$\displaystyle C3 220 = 100m + b$

$\displaystyle 50m = 100 => m = 2 => b = 20$

Thus, the equation is $\displaystyle C = 2n + 20$

Ok, done, simple enough.

What is the signifigance of b?

B indicates a fixed cost, not dependent on N, such as a Base rental fee.

Use the formula to fill in the table.

People Cost

1 $22

2 $24

3 $26

4 $28

What kind of sequence is illustrated in this table?

an arithmetic sequence, aka a linear sequence

The manager tells Monica that during the last 40 days, the hall has been rented 40 times. The number of guests for those 40 rentals can be arranged to form the following sequence:

11,12,13, ..., 49,50

What is the total amount of money collected by the hall manager for those 40 days?