Question 1208784
<pre>
Adam, Ben and Calvin had a total of 540 marbles. Adam gave 1/4 of his marbles to Ben. Then, Ben gave 1/3 of his total number of marbles to Calvin. In the end, all the boys had the same number of marbles.
(a) How many marbles did each boy have in the end? 
(b) How many marbles did Ben have at first?

The number of marbles REMAINED the SAME throughout all the back-and-forth exchanges.
Since the total number they began with was 540, and since ALL 3 ended up with the same number,
<font color = red><font size = 4><b>each ended up with </font></font></b>{{{540/3}}} = <font color = red><font size = 4><b>180 marbles</font></font></b>.

Now, let amount Adam and Ben started with, be A and B, respectively
After Adam gave {{{1/4}}} of his marbles to Ben, Adam then had {{{matrix(1,5, (1 - 1/4)A, "=", (3/4)A, or, 3A/4)}}} remaining
Since Adam had 180 remaining after his exchange with Ben, we get: {{{matrix(2,3,  3A/4, "=", 180, 3A, "=", 4(180))}}}
                                      Amount Adam started with, or {{{matrix(1,7, A, "=", 4(180)/3, "=", 4(60), "=", 240)}}}

After receiving {{{1/4}}} of Adam's marbles, or {{{A/4}}}, Ben then had {{{B + A/4}}}. But, after giving {{{1/3}}} of his
REMAINING marbles to Calvin, Ben then had {{{matrix(1,5, (1 - 1/3)(B + A/4), "=", (2/3)(B + A/4), "=", 2B/3 + A/6)}}} remaining

As Ben had 180 remaining after his exchanges with Adam and Calvin, we get: {{{matrix(1,3, 2B/3 + A/6, "=", 180)}}}
                                                                         {{{matrix(1,3, 2B/3 + 240/6, "=", 180)}}} -- Substituting 240 for A
                                                                          {{{matrix(3,3, 2B/3 + 40, "=", 180, 2B/3, "=", 140, 2B, "=", 3(140))}}}

                                              <font color = red><font size = 4><b>Amount Ben started with</font></font></b>, or {{{matrix(1,7, B, "=", 3(140)/2, "=", 3(70), "=", highlight(highlight(210)))}}}</pre>