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.