Answer:
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
