SOLUTION: A Prince picked a basket full 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

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Question 1163025: A Prince picked a basket full 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 of the apples the prince now had plus two more. The prince paid him and set off again. Just before leaving the enchanted orchard, a third troll stopped him and demanded one-half of his remaining apples plus two more. The prince paid him and sadly went home. He had only two golden apples left.
(a) How many apples had he picked? (show all your workings)
Found 2 solutions by ankor@dixie-net.com, Boreal:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A Prince picked a basket full of golden apples in the enchanted orchard.
let a = original no. of apples
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 - .5a - 2 = (.5a-2) apples remaining
:
A little further on, he was stopped by a second troll guard.
This troll demanded payment of one-half of the apples the prince now had plus two more.
The prince paid him and set off again.
.5(.5a-2) - 2 = .25a-1-2 = (.25a-3) remaining
:
Just before leaving the enchanted orchard, a third troll stopped him and demanded one-half of his remaining apples plus two more.
The prince paid him and sadly went home.
.5(.25a-3) - 2 = .125a - 1.5 - 2 = (.125a-3.5) remaining
He had only two golden apples left.
.125a - 3.5 = 2
.125a = 2 + 3.5
.125a = 5.5
a = 5.5/.125
a = 44 apples picked

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
He had two left.
He had eight before the third troll (gave half + 2 more).
he had 20 before the second troll
He had 44 before the first troll.
start with 8x+16 apples, so can easily divide by 2
gives away 4x+8+2 and now has 4x+6 apples
gives away 2x+3+2 and now has 2x+1 apples
gives away x+0.5+2 and now has x-1.5 apples=2
therefore 2x-3=4
2x=7 apples
8x=28 apples
8x+16=44 apples.