Question

A group of students is on a sightseeing tour.

The total fare is $120 and this is to be shared equally among the students.
If two more students join the tour, each will pay $2 less.
Find the original number of students in the group.​

Answer 1

Given:

A group of students is on a sightseeing tour. The total fare is $120 and this is to be shared equally among the students. If two more students join the tour, each will pay $2 less.

Objective:

To obtain the original number of students in the group.

Step-by-step explanation:

Let x = the original number of students

Trip cost, 120 dollars.

Each Student's price

`(120)/(x)`

If x+2 students, then 2 dollars per student is less. therefore we can write:

`(120)/(x+2) =(120)/(x) -2`

The left part is the price if two more students, and the right part is the original student price minus $2.

They are equal.

Further, the solution is as follows:

`(120)/(x+2) =(120)/(x) -2\\x(x+2)((120)/(x+2) )=x(x+2)((120)/(x) -2)\\120x=120(x+2)-2x(x+2)\\120x=120x+240-2x^(2) -4x\\2x^(2) +4x-240=0\\x^(2) +2x-120=0\\x^(2) +12x-10x+120=0\\(x+12)(x-10)=0`

Further the solution is as follows:

`x+12=0\\x=-12\\x-10=0\\x=10`

As x denotes the number of students in the group it cannot be negative.

Therefore the value of x is 10.

Final Answer:

The original number of students in the group is 10.