Question 1206052
<pre>
Hi
Ryan had $120 more than Kaden. Kaden had 1/4 as much as Ryan. Both of them spent a total of $170. As a result Kaden had 2/3 as much as Ryan. 
A) how much did they have altogether in the end. 
B) how much did Kaden have in the end.

Let original amount Kaden had, be K
Ryan had $120 more than Kaden. so original amount Ryan had, was K + 120
Also, Kaden had {{{1/4}}} as much as Ryan, so original amount Ryan had, was 4K
             We now get: K + 120 = 4K
                             120 = 4K - K
                             120 = 3K
Original amount Kaden had, or {{{matrix(1,5, K, "=", 120/3, "=", "$40")}}}
Original amount Ryan had: 40 + 120, or 4(40) = $160

Total amount they had, originally: $40 + $160 = $200
Since they spent a total of $170, <font color = red><font size = 4><b>remainder was</font></font></b> $200 - 170 = <font color = red><font size = 4><b>$30</font></font></b>


Let Kaden's remainder be K<sub>r</sub> 
Since in the end, Kaden had {{{2/3}}} as much as Ryan, then Ryan's remainder was {{{3/2}}} of Kaden's, or {{{(3/2)K[r]}}}
With total remainder being $30 (see above), we get: {{{matrix(1,3, K[r] + (3/2)K[r], "=", 30)}}} 
                                                      {{{matrix(1,3, 2K[r] + 3K[r], "=", 60)}}} ------ Multiplying by LCD, 2
                                                           {{{matrix(1,3, 5K[r], "=", 60)}}} 
                                  <font color = red><font size = 4><b>Kaden's remainder</font></font></b>, or {{{highlight_green(matrix(1,5, K[r], "=", 60/5, "=", highlight("$12")))}}}</pre>