a prince picked a basketful of golden apples in the enchanted orchard. one 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 agian. a little farther on, he was stopped by a second troll guard. this troll demande payment of one-half of the apples the prince now had plus two more. the prince paid him and set off agian. just before leavingthe enchanted orchard, a third troll stopped hiom and demanded one half of his remaining apples plus two more. the prince paid him and sadly went home. he had only two apples left.
i need help on how to do this and find out how many apples he picked
2006-09-17 17:03:41 · 8 answers · asked by t t 1 in Education & Reference ➔ Homework Help
Working backwards. Let's say he could get back all his apples.
he had two apples left: he took 2 (=4) plus double (=8) from troll #3
Then he took 2 (=10) plus double (=20) from troll #2
Then he took 2 (=22) plus double (=44) from troll #1
44 in total.
Edit:
Just to double check:
start: 44 apples
troll 1: gave 22 away plus another 2, now has 20
troll 2: gave 10 away plus another 2, now has 8
troll 3: gave 4 away plus anothe 2, now has 2.
Tada!
2006-09-17 17:10:19 · answer #1 · answered by borscht 6 · 1⤊ 0⤋
Poor prince. Set up your basic equation: 1/2x + 2. That translates to "one half of the apples plus two more." The x stands for the number of apples. Keep that in mind.
Then you'll have to work backwards. You know at the end he had 2 left.
So here we go: 2x+2 is how many apples he had before that last troll took some. So plug in the two. You get 4+2=6.
That takes care of troll #3. But we still have to take care of trolls # 1 and 2. So do that same 2x+2 thing again.
Troll #2: 2(6) +2 = 14
Troll #1: 2(14)+2= 30
30 is how many apples the prince had before the whole troll thing started.
This problem looks tricky because you have to work backwards. Always start by translating whatever info you have into some sort of an equation, then go from there. Hope that cleared things up a bit!
2006-09-18 00:13:16 · answer #2 · answered by kacey 5 · 0⤊ 0⤋
Start off with what is left. He has two, and he gave the last troll 2 plus half the apples. So take the two the prince has plus the remaining two, add them up to get four, and double it to get eight. In other words... when he got to the last troll, he had 8 apples. The troll wanted half the apples plus two more. 8 divided by 2 is four, take away 2 more and there's two left. Just keep working your way back through the trolls. Add the "two more" to what you have, and double it to get what you started with.
:) I won't give you the answer because it's your homework and all but this should get you going in the right direction!
2006-09-18 00:14:51 · answer #3 · answered by dcgirl 7 · 0⤊ 0⤋
total apples is 44.
consider A is total apples the prince paid the same for 3 times.. lets start wit the first.. (A/2 -2)= (A-4)/2
now this fraction is the new number devide it by 2 and minus 2 gives you (A-12)/4 take this one and do the same thing devide it by 2 and minus 2 gives you (A-28)/8. At the end the prince is left with 2 apples so you solve the eqaution (A-28)/8=2 gives you 44 apples.
2006-09-18 00:30:38 · answer #4 · answered by some1 1 · 0⤊ 0⤋
a is how many apples he had originally
1/2a-2 is what you have left after the first troll
1/2(1/2a-2)-2 is what you have left after the second troll
1/2[1/2(1/2a-2)-2]-2 is what you have left after the third troll.
Set that equal to 2 and solve.
Hope this helps. Good Luck.
2006-09-18 00:07:22 · answer #5 · answered by SmileyGirl 4 · 1⤊ 0⤋
I see other gave the answer so i will take 2 points good luck
2006-09-18 00:13:17 · answer #6 · answered by robert899295 3 · 0⤊ 0⤋
(1/2 + 2) + (1/2 + 2) + (1/2 + 2) + 2 =9.5 ?
2006-09-18 00:11:30 · answer #7 · answered by Shar-Ching 3 · 0⤊ 1⤋
Nice one. borscht got it right,
T T thanks for the two points
Njoy....
2006-09-18 00:19:36 · answer #8 · answered by sanghvir 3 · 0⤊ 0⤋