At final, Kaden and Dan have the same amount of 240 dollars: the total does not change, right?

And at final, they have equal amounts, righ?

    Hence, at the end each of them has 120 dollars.



Next, Kaden's final amount of 120 dollars is 4/5 of what Kaden had initially.

    It implies that 1/5 of what Kaden had initially  is 120/4 = 30 dollars.
        Hence, the amount which Kaden had initially, was 5*30 = 150 dollars,
          and  the amount which Dan   had initially, was 240 - 150 = 90 dollars.



At this point, the problem is just solved.



ANSWER, Initially, Dan had $90.

Hi
Kaden and Dan had a total of $240 . Kaden gave 1/5 to Dan. As a result both had the same amount of money in the end. How much did Dan have at first. 
 
Thanks
PS my son couldn't solve this problem. Ie no solution 

Let original amount Dan had be D
Then original amount Kaden had = 240 - D
After Kaden gave Dan  of his amount, Kaden then had  remaining
After receiving  of Kaden's, Dan then had 

Since after this exchange, they both had the same amount, then we get: 
                                                                         960 - 4D = 5D + 240 - D -- Multiplying by LCD, 5
                                                                        960 - 240 = 4D + 4D
                                                                              720 = 8D
                                                   Original amount Dan had, or