Question 1185956
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When each brother eats 2/3 of the biscuits, 1/3 of them are left.  So when each brother eats some of the biscuits, the number of biscuits remaining gets multiplied by 1/3 and the reduced by 1/3.  So<br>
original number of biscuits: {{{x}}}<br>
number after Roy eats his: {{{(1/3)x-1/3}}}<br>
number after Sam eats his: {{{(1/3)((1/3)x-1/3)-1/3}}}<br>
number after Tom eats his: {{{(1/3)((1/3)((1/3)x-1/3)-1/3)-1/3}}}<br>
The number of biscuits left at the end is 0, so<br>
{{{(1/3)((1/3)((1/3)x-1/3)-1/3)-1/3=0}}}<br>
That equation is actually not too hard to solve, although it is easy to get lost along the way....<br>
This kind of problem is quite often easier to work backwards, especially if there are a large number of steps.  (Imagine what the final equation above would look like if there had been five (or more) brothers.)<br>
At each step working the problem from beginning to end, the number of biscuits remaining is multiplied by 1/3 and then 1/3 is subtracted.  Working that backwards, each step consists of adding 1/3 to the number remaining (the opposite of subtracting 1/3) and multiplying that by 3 (the opposite of dividing by 3).<br>
Working the problem backwards is then simple:<br>
biscuits remaining at the end: 0
biscuits remaining before Tom eats his: 3(0+1/3) = 3(1/3) = 1
biscuits remaining before Sam eats his: 3(1+1/3) = 3(4/3) = 4
biscuits remaining before Roy eats his: 3(4+1/3) = 3(13/3) = 13<br>
There were 13 biscuits originally; Roy ate 9.<br>
ANSWER: Roy ate 9 biscuits<br>