SOLUTION: This is a question from a packet i am supposed to do over the summer. A prince packed a basket of golden apples in the enchanted orchard. On his way home, he was stopped by a tro

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Question 89530: This is a question from a packet i am supposed to do over the summer.
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?
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you can probably think backwards from the two apples the prince is left with and arrive at a solution

here is the equation ... apples=(((((2+2)*2)+2)*2)+2)*2 ... so apples=44

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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!