Problem Solving

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

Please explain how the below answer is found.

The answer is Sx/ T(T-S)

Lookingfor700GMAT wrote:To celebrate a colleague's retirement, the T coworkers in an office agreed to equally share the cost of a catered lunch. If the lunch cost a total of x dollars and S of the coworkers, fail to pay their share, what is the expression which represents the additional amount in dollars that each of the remaining coworkers would need to contribute so that cost of the lunch is completely paid?

Please explain how the below answer is found.

The answer is Sx/ T(T-S)

total payment=x
total workers=t
per head cost=x/t(original cost)

new strength of workers sharing the cost=t-s
per head=x/(t-s)[increased cost ]

now additional cost for wokers is= increased cost - original cost
=x/(t-s)-x/t=sx/[t(t-x)]

This problem is best solved by using numbers ok:

Now let T (Total Co-workers) = 10
X (Cost of lunch) = 100
S (Co-workers who refuse to pay) = 5

Now:
Cost per worker = X/T = 100/10 = 10
Actual amount paid by workers willing to pay = 100/(10-5) = 20
Therefore additional amount paid by workers who paid = 20 - 10 = 10(a)

SX/T(T-S) = 5*100/10(10-5) = 500/50 = 10(a)

(a) = (a) therefore SX/T(T-S) is correct!!

Lookingfor700GMAT wrote:To celebrate a colleague's retirement, the T coworkers in an office agreed to equally share the cost of a catered lunch. If the lunch cost a total of x dollars and S of the coworkers, fail to pay their share, what is the expression which represents the additional amount in dollars that each of the remaining coworkers would need to contribute so that cost of the lunch is completely paid?

Please explain how the below answer is found.

The answer is Sx/ T(T-S)

When T coworkers were to equally share in $x, each should have contributed $x/T. If S (assumably < T) of the coworkers fail to pay their share, the $x must be equally shared by (T - S) coworkers and each would now have contributed $x/(T - S). Hence, the additional amount in dollars that each of the remaining coworkers would need to contribute

= ${x/(T - S) - (x/T)}

= ${S x/ T (T - S)}