If p of the coworkers fail to contribute, which represents the additional amount that each of the remaining coworkers must contribute to pay for the lunch?

Question

The whole question:

To celebrate a colleague's graduation, the m coworkers in an office agreed to contribute equally to a catered lunch that costs a total of y dollars. If p of the coworkers fail to contribute, which of the following represents the additional amount, in dollars, that each of the remaining coworkers must contribute to pay for the lunch?

 

A. y/m

B. y/(m-p)

C. py/(m-p)

D. y(m-p)/p

E. py/m(m-p)

 

Please help. Thank you.

Answer 1

This problem looks familiar--is it from the SAT "Blue book"?

 

It can be solved by substituting values:

 

Let's try y = 100, m = 10, p = 4

 

If everyone contributes, then each person pays 100/10 = $10

If 4 people don't contribute, then the $100 is divided 6 ways for a per person cost of $16.67.

 

So, the additional amount paid per person is 16.67 - 10 = $6.67

 

Now, plug the chosen values into each answer choice and look for an answer equal to $6.67:

 

(A). y/m = 100/10 ≠ $6.67

(B). y/(m-p) = 100/6 ≠ $6.67

(C). py/(m-p) = 400/6 ≠ $6.67

(D). y(m-p)/p = 600/4 ≠ $6.67

(E). py/[m(m-p)] = 400/60 = $6.67

 

ANSWER: (E)

Answer 2

The cost per person the coworkers were originally going to pay is $y / m people = y/m.

 

Now, however, the cost per person is $y / (m-p) people = y/(m-p).

 

The difference between them (which is the additional cost each person owes) is:

 

y/(m-p) - y/m

(ym) / (m(m-p)) - (y(m-p)) / (m(m-p))

(ym - (ym - py)) / (m(m-p))

(ym - ym + py) / (m(m-p))

(py) / (m(m-p))