Question 1201639
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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 {{{1/5}}} of his amount, Kaden then had {{{matrix(1,3, (4/5)(240 - D), or, 4(240 - D)/5)}}} remaining
After receiving {{{1/5}}} of Kaden's, Dan then had {{{matrix(1,3, D + (1/5)(240 - D), or, D + (240 - D)/5)}}}

Since after this exchange, they both had the same amount, then we get: {{{matrix(2,3, 4(240 - D)/5, "=", D + (240 - D)/5, (960 -  4D)/5, "=", D + (240 - 
D)/5)}}}
                                                                         960 - 4D = 5D + 240 - D -- Multiplying by LCD, 5
                                                                        960 - 240 = 4D + 4D
                                                                              720 = 8D
                                                   Original amount Dan had, or {{{highlight_green(matrix(1,5, D, "=", 720/8, "=", highlight("$90")))}}}</pre>