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

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) (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) (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.
RELATED QUESTIONS
A Prince picked a basketful of golden apples in the enchanted orchard. On his way home,... (answered by josmiceli,rapaljer)
This is a question from a packet i am supposed to do over the summer. A prince packed a (answered by scott8148,ankor@dixie-net.com)
a man passed through into an orchard, where he picked a certain number of apples. On the... (answered by Edwin McCravy)
Rebecca picked 4/9 of a basket of apples yesterday. Today she picked 1/6 of a basket of... (answered by josgarithmetic)
In an enchanted garden there was a miracle tree. It had 25 bananas and 30 oranges.... (answered by KMST,ikleyn)
Bill and his cousin Bella are picking apples in their grandparents' orchard. Bill has... (answered by josgarithmetic,Boreal)
Bill and his cousin Bella are picking apples in their grandparents' orchard. Bill has... (answered by Solver92311)
a basket has both red and green apples. the shaded section of the strip diagram... (answered by Fombitz)
kado, chado and nado are good friends in the village. one day, kado on his way to village (answered by greenestamps)