Question

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 the n employees who attended the dinner, each of the k + 1 employees would have paid $18.

Answer 1

$342

Explanation:

Let the total cost of the dinner = C

If it was shared equally by k employees who attended the dinner and each of the k employees who shared the cost of the dinner paid $19.

We have:

`(C)/(k)=19 \\\\C=19k`

If the total cost(C) had been shared equally by k + 1 employees who attended the dinner, each of the k + 1 employees would have paid $18.

This written mathematically is:

`(C)/(k+1)=18 \\\\C=18(k+1)`

Equating the cost, C from both equations

19k=18(k+1)

19k=18k+18

19k-18k=18

k=18

Therefore, the total cost of the dinner,

C=19k

=19 X 18

=$342