SOLUTION: 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 Php. 100. How many peop

Question 393661: 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 Php. 100. How many people actually joined the outing? (Show Your Solution)
Found 2 solutions by mananth, stanbon:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
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 Php. 100. How many people actually joined the outing? (Show Your Solution)
...
the total outing cost for a group of people amounted to P8000. when an additional 4 persons decided to join the outing, the cost per person decreased by P100. how many actually joined the outing?
...
let there be x persons
cost per person = 8000/x
..
4 persons join
=x+4
cost reduces by 100
..
8000/x - 8000/(x+4)= 100
LCD = x(x+4)
(8000(x+4)-8000x)/x(x+4)=100
8000x+32000-8000x=100(x(x+4))
32000=100x^2+400x
/100
320=x^2+4x
x^2+4x-320=0
x^2+20x-16x-320=0
x(x+20)-16(x+20)=0
(x-16)(x+20)=0
x= 16 which is positive
Initially 16 persons joined the outing.
...
m.ananth@hotmail.ca

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The total outing cost for a group of people amounted to Php. 8000.
------------
Original DATA:
Let number in the group be "x".
Average cost per person is 8000/x Php.
-----------------------------
When an additional 4 persons decided to join the outing, the cost per person decreased by Php. 100.
New DATA:
Number in the group is "x+4".
Average cost perperson is 8000/(x+4) Php.
--------------
How many people actually joined the outing?
Equation:
original average - new average = 100 Php
8000/x - 8000/(x+4) = 100
---
Divide thru by 100 to get:
80/x - 80/(x+4) = 1
-----------------------
Multiply thru by x(x+4) to get:
80(x+4) - 80x = x(x+4)
80*4 = x^2+4x
---
x^2+4x-320 = 0
(x-16)(x+20) = 0
---
Positive solution:
x = 16 (original # of people in the group)
===============
Cheers,
Stan H.
RELATED QUESTIONS
the total outing cost for a group of people amounted to P8000. when an additional 4... (answered by mananth)
The total outing cost for a group of people amounted to PhP8000. When an additional four... (answered by ikleyn)
A civic club charters a bus for one day at a cost of $575. When 2 more people join the... (answered by Fombitz)
The cost of hiring a bus for an outing is $240 and this was to be shared by the x people. (answered by josgarithmetic)
The cost of hiring a bus for an outing was $240 and this was to be shared equally by X... (answered by josgarithmetic)
A group of friends planned a trip and chartered a bus for 300$. When 3 more friends... (answered by Stitch)
The Cruz family went to an outing in a mountain resort. Mrs. Cruz gave to the cashier (answered by ikleyn)
A group of people could rent a social hall for $480. When 14 more people join the... (answered by stanbon)
A family wants to attend a concert. The admission fee is R50 for an adult and R20 for a... (answered by ikleyn)