Problem Solving

The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner?
(1) Each of the k employees who shared the cost of the dinner paid $19.
(2) If the total cost of the dinner had been shared equally by k+1 of then employees who attended the dinner, each of the k + 1 employees would have paid $18.

Let C = total cost
Let K= number of people sharing cost
Let P = per person shared cost

Therefore, P = C/K and C = P x K > if we can discover what P and K are, then we know C

Statement 1: Indicates that P = 19, therefore C/K = 19 > tells us nothing about C

Statement 2: Indicates that P = 18 = C/ (K+1) > also tells us nothing about C

Can the statements taken together tell us about C ?

Statement 1 can be rearranged as follows: K = C/19

Substitute that into Statement 2: C/(C/19+1)= 18

Rearrange: 19C/(C+19) = 18

19C = 18C + (18*19)

Therefore C = 18*19 > Both statements together provide the answer