Question

A trip to Europe for a class of n students has a fixed cost of x dollars. If 5 students decide not to go, then how much more will it cost each student to take the trip?

A) x/5
B) x/n-5
C) (x/n)-(x/5)
D) (x/n)-(x/n-5)
E) (x/n-5)-(x/n)

Answer 1

n students, fixed cost = x dollars.

Originally each student to contribute = x/n

If 5 , decide not to go, the number left = (n - 5)

Cost = x/(n - 5)

The extra cost is x/(n - 5) - x/n

Option E.

Answer 2

Answer would be E) (x/n-5) - (x/n).

$x is fixed and the cost is shared with the whole class.

Whole Class = n

So, if 5 students decides to remove themselves from the trip ...

Whole class - 5 students = n - 5

If $x is shared with (n-2) students, each students has to pay ...

$(x/n-2)

But the question wants to know how much MORE each student has to pay ...

Adjusted cost - Original cost = $(x/n-2) - $(x/n)

Why $(x/n-2) - $(x/n) ?
$(x/n-2) will incur more cost for each student than $(x/n) as it is divided by a smaller denominator.

Imagine if lesser students went for the trip but has to pay the same amount for their trip. Wouldn't each of them have to pay more?