Question

A social club charters a bus at a cost of $2805 to take a group of members on an excursion to Atlantic City. At the last minute, 4 people in the group decide not to go. This raises the transportation cost per person by $4. How many people originally intended to take the trip?

Answer 1

so how many people were originally intended to take the trip?

Answer 2

o ok

Answer 3

its a long solution and so had to send in two parts....☺

Answer 4

i appreciate it ugh.. i chose the wrong version its supposed to be A social club charters a bus at a cost of $7350 to take a group of members on an excursion to Atlantic City. At the last minute, 1 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

Answer 5

the numbers all switched. is there anyway for you to figure that out quick

Answer 6

well...
let me see.....

Answer 7

so once again lol how many were orginally intended

Answer 8

wait more coming...

Answer 9

k

Answer 10

?

Answer 11

geez crazy equation

Answer 12

?

Answer 13

sorry friend....

i seem to have made some mistakes in the solution...
give me your email id and ill send the solution in a few minutes for both questions.....

Answer 14

its alright

Answer 15

i just need to know how many people orginally intended to take the trip

Answer 16

just send it on here or too gfoste00@leeu.edu if thats easier

Answer 17

then b patient, i'll post the solution in five minutes...

Answer 18

k

Answer 19

are you posting it on he?

Answer 20

here*

Answer 21

yes, I am first posting for the first question which I had solved wrong.....

Answer 22

let the total number of people originally = x
let the money paid by each person = y

x*y = 2805 -------------- (1)

2805
y = -------- -----------(2)
x

when 4 member do not go, then members going = x-4
now money these (x-4) members have to pay = (y + 4)

(x-4)(y+4) = 2805
xy - 4y + 4x - 16 = 2805
Substituting value of xy from (1)
2805 – 4y + 4x – 16 = 2805
2789 – 4y + 4x = 2805
-4y + 4x = 2805 – 2789
-4y + 4x = 16
4(-y + x) = 16
-y + x = 16/4
Substituting value of y from (2)

Answer 23

-2805
------ + x = 4
x
-2805 + x²
---------- = 4
x

-2805 + x² = 4x
x² - 4x - 2805 = 0
x² - 55x + 51x - 2805 = 0
x(x-55) +51(x-55)=0
(x - 55)(x + 51) = 0

if x - 55 = 0 => x = 55
if x+51 = 0 => x = -51 (we ignore this value as number of people cannot be negative)

so number of people originally taking the trip was 55

Answer 24

now I'll post for the second one in a couple of minutes.....

Answer 25

so the final answer is?

Answer 26

wait this isnt even the right one. i need the solution for the one with 7805

Answer 27

this one : A social club charters a bus at a cost of $7350 to take a group of members on an excursion to Atlantic City. At the last minute, 1 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

Answer 28

let the total number of people originally = x
let the money paid by each person = y

x*y = 7350 -------------- (1)

7350
y = -------- -----------(2)
x

when 1 member does not go, then members going = x-1
now money these (x-1) members have to pay = (y + 3)

(x-1)(y+3) = 7350
xy - y + 3x - 3 = 7350
Substituting value of xy from (1)
7350 – 3 -y + 3x = 7350
- y + 3x = 7350 - 7347
- y + 3x = 3

Answer 29

more follows...

Answer 30

Substituting value of y from (2)

- 7350
------ + 3x = 3
x

-7350 + 3x²
----------- = 3
x

-7350 + 3x² = 3x
3x² - 3x - 7350 = 0
3[x² - x - 2450] = 0
3[x² -50x + 49x - 2450] = 0
3[x(x - 50) +49(x - 50)] = 0
3(x - 50)(x + 49) = 0

Answer 31

if x-50 = 0, then x = 50
if x+49 = 0,then x = -49 (we ignore this value as number of people cannot be negative)

so the number of people originally going on the trip was 50