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?
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!
thanks Reiny, hope i am as intelligent as you.... :)
To solve this problem, let's break it down step by step.
Let's assume the initial number of people who joined the trip is 'x'. So initially, the total cost for 'x' people is Php 8000.
We know that when an additional 4 persons joined the outing, the cost per person decreased by 100. This means that the cost per person after the additional 4 persons joined is '100' less than the previous cost per person.
Let's find the previous cost per person:
Previous cost per person = Total cost / Number of people
Previous cost per person = 8000 / x
Now, let's find the new cost per person:
New cost per person = Total cost / (Number of people + Additional persons)
New cost per person = 8000 / (x + 4)
According to the given information, the new cost per person is '100' less than the previous cost per person. So we can set up the equation:
8000 / (x + 4) = 8000 / x - 100
To solve this equation, we can multiply both sides by 'x' to eliminate the denominator:
8000x = 8000(x + 4) - 100x
Expanding and simplifying the equation:
8000x = 8000x + 32000 - 100x
Next, we can cancel out '8000x' from both sides:
0 = 32000 - 100x
Solving for 'x', we get:
100x = 32000
x = 32000 / 100
x = 320
Therefore, initially, 320 people joined the trip.