Question

The total outing cost for a group of people amounted to Php 8000. When an additional 4 persons decided to join the outing, the cost per person decreased by 100. How many people actually joined the trip?

Answer 1

let number of people originally be n
cost per person = 8000/n

new count = n+4
new cost = 8000/(n+4)

8000/n - (8000/(n+4) = 100
times n(n+4)
8000(n+4) - 8000n = 100n(n+4)
expand after dividing by 100
80n + 320 - 80n = n^2 + 4n
n^2 + 4n - 320 = 0
(n+20)(n-16) = 0
n = 16 or n=-20 , but clearly n > 0

so originally 16 people had signed up, but 4 more joined,
So there were 20 people on the trip

check:
original cost = 8000/16 = 500
new cost = 8000/20 = 400
YUP!

Answer 2

thanks Reiny, hope i am as intelligent as you.... :)