Jawaban:

Let's assume the total sum of money they shared is $x.

According to the ratio, Roy received 4x/24 of the total sum, Shirley received 9x/24, and Tim received 11x/24.

Shirley had $100 more than Roy, so Roy received 4x/24 - $100.

So, the total amount of money received by Roy and Shirley is 4x/24 - $100 + 9x/24 = 13x/24 - $100.

Since they shared the whole sum of money, we can set the equation:

x = 13x/24 - $100 + 11x/24

24x = 24 * (13x/24 - $100) + 24 * (11x/24)

24x = 13x - $2400 + 11x

24x = 24x - $2400

$2400 = 0

Therefore, Tim had $11x/24 of the total sum, which is $11x/24 = $0.