SOLUTION: A Prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll. The troll demanded payment of one-half of the apples plus two mor
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Question 213456: A Prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll. The troll demanded payment of one-half of the apples plus two more. the prince gave him the apples and continued on home. The prince was then stopped by a second troll who demanded one- half of the apples plus two more, the prince did as he was told and continued on home. Stopped by a third troll he demanded the prince give him one- half of the apples plus two more. The prince did as asked and sadly continued on home only having two golden apples left. How many apples did he pick to begin with?
Found 2 solutions by josmiceli, rapaljer:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of apples he started with
After 1st troll:
He has
After 2nd troll:
He has
After 3rd troll:
He has
and the problem says:
Add to both sides
Multiply both sides by
Add to both sides
Multiply both sides by
Add to both sides
The Prince picked 44 apples
check answer:
1st troll took
which left the Prince
2nd troll took
which left the prince
3rd troll took
Which left the Prince
OK
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = total number of apples
The first troll demands half of his apples plus 2, so after leaving the first troll, the prince has
apples
The 2nd troll demands half of what is left and 2 more, so now the prince has
The 3rd troll demands half of what is left and 2 more, so now the prince has
And this equals exactly 2 apples!
Now, work this backwards by adding +2 to each side:
Multiply both sides by 2:
(1/4)x-3=8
Add +3 to each side:
(1/4)x=11
Multiply both sides by 4:
x=44 apples.
Check: If the prince starts with 44 apples, the first troll gets 22 +2 =24 apples. The prince is left with 20. The second troll demands 10+2, which leaves the prince with 8. The third troll demands 4 apples plus 2, leaving the prince with 2 apples.
Very nice problem!! Poor princess!!
R^2
Dr. Robert J. Rapalje, Retired
Seminole Community College
Altamonte Springs Campus
Florida
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