<PRE><B>Question 89530</B>
A prince packed a basket of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded the orchard. The troll demanded payment of one-half of the apples, plus two more. The prince gave him the apples and set off again. A little further on, he was stopped by a second troll guard. This troll demanded payment of one-half the apples, plus two more. The prince paid him and set off again. A third troll stopped him and demanded one-half of the apples plus two more. The prince now has two apples left. How many apples did he pick?
:
Let x = number of apples picked
:
1st Troll payment:
x - (.5x + 2): simplify
x - .5x - 2
(.5x - 2) remaining
:
2nd troll payment
(.5x-2) - (.5(.5x-2)+ 2)
(.5x - 2) - (.25x - 1 + 2)
(.5x - 2) - (.25x + 1)
.5x - 2 -  .25x - 1
.25x - 3 remaining
:
3rd troll payment
(.25x - 3) -(.5(.25x-3)+2) = 2
(.25x - 3) -(.125x - 1.5 + 2) = 2
(.25x - 3) -(.125x + .5) = 2
.25x - 3 - .125x - .5  = 2
.125x - 3.5 = 2
.125x = 2 + 3.5
.125x = 5.5
x = 5.5/.125
x = 44 apples
:
Check:
 44
-24; (22+2)
-----
 20
-12; (10+2)
-----
  8
 -6; (4+2)
------
  2 remaining 
:
Hope this made some sense to you!
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