Question 213456
Let {{{a}}} = number of apples he started with
After 1st troll:
He has {{{a/2 - 2}}}
After 2nd troll:
He has {{{(a/2 - 2)/2 - 2}}}
After 3rd troll:
He has {{{((a/2 - 2)/2 - 2)/2 - 2}}}
and the problem says:
{{{((a/2 - 2)/2 - 2)/2 - 2 = 2}}}
Add {{{2}}} to both sides
{{{((a/2 - 2)/2 - 2)/2 = 4}}}
Multiply both sides by {{{2}}}
{{{(a/2 - 2)/2 - 2 = 8}}}
Add {{{2}}} to both sides
{{{(a/2 - 2)/2 = 10}}}
Multiply both sides by {{{2}}}
{{{a/2 - 2 = 20}}}
Add {{{2}}} to both sides
{{{a/2 = 22}}}
{{{a = 44}}}
The Prince picked 44 apples
check answer:
1st troll took {{{44/2 + 2 = 24}}}
which left the Prince {{{44 - 24 = 20}}}
2nd troll took {{{20/2 + 2 = 12}}}
which left the prince {{{20 - 12 = 8}}}
3rd troll took {{{8/2 + 2 = 6}}}
Which left the Prince {{{8 - 6 = 2}}}
OK