Question 1193163

Hi
Jane gave a third of her beads and another 4 more to Sally, a third of the remaining beads and 3 more to Mary and a third of the rest plus 3 to betty. 
In the end she had 3 beads left. How many did she have at first. 
Thanks
<pre>Let original number be J
After giving {{{1/3}}} and another 4 to Sally, she had {{{matrix(1,3, (2/3)J  -  4, or, 2J/3  -  4)}}} left 
After giving {{{1/3}}} and another 3 of the REMAINDER to Mary, she had {{{matrix(1,3, (2/3)(2J/3  -  4) - 3, or, 4J/9  -  8/3 - 3)}}} left 
After giving {{{1/3}}} and another 3 of the REMAINDER to Betty, she had {{{matrix(1,7, (2/3)(4J/9  -  8/3 - 3) - 3, ",", or, 8J/27  -  16/9  -  2 - 3, ",", or, 8J/27  -  16/9  -  5)}}} left 
Since she had 3 beads in the end, we get: {{{matrix(1,7, 8J/27  -  16/9  -  5, "=", 3, or, 8J/27 - 16/9, "=", 8)}}}
8J - 48 = 216 ------- Multiplying by LCD, 27
8J = 264
Original number of beads, or {{{highlight_green(matrix(1,5, J, "=", 264/8, "=", highlight(33)))}}}</pre>