A social club charters a bus at a cost of $1020 to take a group of members on an excursion to Atlantic City. At the last minute, nine people in the group decide not to go. This raises the transportation cost per person by $3. How many people originally intended to take the trip?

60 people originally intended to take the trip

Explanation:

The original total cost for chartering a bus is $1020 to take a group member to Atlantic City. 9 people opted not to go and this raises the cost per person to $3.

The actual arrangement for the trip

Let

a = cost per person for the trip

b = number of people for the trip

therefore

ab = 1020 ... (i)

After 9 people opted not to go

cost per person = a + 3

number of people for the trip = b - 9

(a + 3) (b - 9) = 1020 ... (ii)

ab - 9a + 3b - 27 = 1020

since ab = 1020

-9a + 3b - 27 = 0

9a = 3b - 27

divide through by 9

a = 1/3b - 3

insert a in equation (i)

ab = 1020

(1/3b - 3) b = 1020

b²/3 - 3b = 1020

multiply through by 3

b² - 9b = 3060

b² - 9b - 3060 = 0

two numbers one can multiply to get - 3060 is - 60 and 51. when you add both of them you get - 9

(b - 60) (b + 51)

therefore

b = 60 or - 51

60 is positive so we use 60

b = 60

60 people originally intended to take the trip