A catering company charges $550 for 20 guests and $775 for 35 guests.

Question

a) create an equation to represent the relationship between cost and number of guests?

b) determine the total cost of 73 guests?

c) if the total cost is $1635, determine how many guests attended?

Answer 1

C = 550 = 20x + b

C = 775= 35x + b

140x + 7b = 3850

140x + 4b = 3100

3b =750

b = 750/3 = 250

20x = 550-250= 300

x = 30/2 = $15 per person

C(p) = 15p =250

flat fee of $250 plus $15 per person

35x = 775-250 = 525

x = 525/35 = $15 per person

C(73) = 15(73) + 250 = $1,095 for 73 people

1635 = 15p +250

p = (1635-250)/15 = 1385/15= about 92 people at a cost of $1635

had the problem been C=1645

then

p = (1645-250)/15 =1395/15 = 92 people

with 1635, you get 92 1/3 people. Maybe you typed a 3 instead of 4 for the tens digit in 1645