lunch

dreamv wrote:To celebrate a colleague’s retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A.x/t
B.x/(t-s)
C.sx/(t-s)
D.sx/t(t-s)
E.x(t-s)/t

Originally, T people were to pay total cost of x dollars.
So, each person pays x/T each.

After S people drop out, there are T-S people to pay total cost of x dollars.
So, each person pays x/(T-S) each.

The additional amount that each must pay = New cost per person - original cost per person
= x/(T-S) - x/T
Check the answer choices . . . not there. It looks like they want us to combine the two fractions.

So, rewrite with common denominator: x/(T-S) - x/T = xT/[T(T-S)] - [x(T-S)]/[T(T-S)]
= xT/[T(T-S)] - [xT-xS)]/[T(T-S)]
= xS/[T(T-S)]
= D

Cheers,
Brent