Let, Cayden had $x and Jayden had $y.

According to the question,

x + y = 784 ...............(1)

and, x - \({x \over 6}\frac{}{}\) = y - 124

5x - 6y = -744 ................(2)

Solving equation (1) and (2)

eq(1) *6 + eq(2)

6x + 6y = 4704

5x - 6y = -744

...............................................

11x = 3960

x = 360

Therefore, Cayden had $360 at first.