Ok here is the problem:
One night, the King couldnt sleep, so he went down into the kitchen, where he found a bowl of mangoes. Being hungry, he took 1/6 of the mangoes. Later that same night, the queen was hungry and found the mangoes and took 1/5 of what the king had left. Still later, the first prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes. Even later, his brother, the second prince, ate 1/3 of what was left. Finally, the third prince ate 1/2 of what was left, leaving only three mangoes for the servants. How many mangoes were originally in the bowl?
Someone please help me figure this out!!
Thanks!
2007-09-04 09:35:28 · 11 answers · asked by Former Atheist 4 in Science & Mathematics ➔ Mathematics
Each time you take a fraction, what is left is the product of what you had and (1-fraction).
If M is the number of mangoes at the beginning then:
3 = M(1-1/6)(1-1/5)(1-1/4)(1-1/3)(1-1/2)
so 3 = M(5/6)(4/5)(3/4)(2/3)(1/2) = M/6 so M = 18.
There were 18 mangoes at the beginning.
2007-09-04 09:42:50 · answer #1 · answered by Christophe G 4 · 0⤊ 0⤋
alright so let's look at this step by step
there was 3 left in the morning, so the third prince must of had 3 (he took half so what's left is the same as what he took)
before him, the second prince took 1/3 of what was there leaving 2/3 or 6, from that we can tell that the second prince also had 3 (again we look at what's half of 6 to determine what was taken)
the first prince took 1/4 of the mangos leving 3/4 or 9 mangos. to find how many was there before the first prince we multiply 9 by the fration 4/3 and get that there was 12 there and the find out the first prince. like his brothers ate 3 mangos in the night
the queen left 12 mangos or 4/5 of what was there when she found the mangos, so to find what was there we multiply 12 by the fration 5/4 to find that there was 15 before the queen ate her mangnos in the night
the king left 15 mangos or 5/6 of what he found. to find what was there before he got there we mutiply what was left by 6/5 and find that there was 18 to begain the night
to put it in one equation:
5/6*4/5*3/4*3/2*2/1*3=18
2007-09-04 10:00:19 · answer #2 · answered by hunter_o_redheads 3 · 0⤊ 1⤋
Let m be the number of mangoes originally in the kitchen. The King took 1/6m mangoes, leaving 5/6m in the bowl.
The queen then came and took 1/5(5/6m) of the mangoes, leaving 4/5(5/6m), or 2/3m mangoes in the bowl.
The first prince took 1/4(2/3m) mangoes, leaving 3/4(2/3m) or 1/2m mangoes.
The second prince took 1/3(1/2m) mangoes, leaving 2/3(1/2m) or 1/3m mangoes.
The third prince took 1/2(1/3m) mangoes, leaving 1/2(1/3m) or 1/6m mangoes still in the bowl.
The equation to be solved is then 1/6m = 3
which gives m = 18 mangoes originally in the bowl.
Incidentally, each of the royals took 1/6m, or 3 mangoes, from the bowl, as can be verified by simplifying the expression for the number of mangoes each took and replacing 18 for m.
2007-09-04 09:51:17 · answer #3 · answered by devilsadvocate1728 6 · 0⤊ 0⤋
Count the mangoes left each time.
N mangoes to begin with.
The king eats 1/6, 5N/6 remain
The queen eats 1/5, 5N/6*4/5 remain
The first prince eats 1/4, 5N/6*4/5*3/4 remain
The second prince eats 1/3, 5N/6*4/5*3/4*2/3 remain
The third prince eats 1/2, 5N/6*4/5*3/4*2/3*1/2 remain
5N/6*4/5*3/4*2/3*1/2 = N/6 = 3, N=18
There were 18 mangoes in the bowl
2007-09-04 09:43:54 · answer #4 · answered by stym 5 · 0⤊ 0⤋
If there were only 6 you'd be ok, right? (Then the King, Queen, et al) would have taken one each [1/6th; 1/5th; 1/4th, etc.). Since there are three left when third prince had his; why not multiply what is left by 6?, making 18 the number of mangoes when the King had his?
18 to start; King has 1/6th (three) leaving 15 (Queen has 1/5th (three more), leaving 12; (prince has 1/4th [three again!, leaving 9]; 2d prince has 1/3rd (3, leaving 6); last prince has 1/2 (3!, leaving....THREE.).
How's that sound?
2007-09-04 09:45:00 · answer #5 · answered by Goethe's Ghostwriter 7 · 0⤊ 1⤋
18
Each person ate 3 mangoes leaving 3 mangoes at the end.So 15*3 + 3 = 18
2007-09-04 09:51:02 · answer #6 · answered by ironduke8159 7 · 0⤊ 1⤋
You need to work backwards from the known number.
3rd prince eats three leaving three = total he found of 6
2nd prince eats 1/3 leaving 2/3 = 6 ; total he found was 9
1st prince eats 1/4 leaving 3/4 = 9 ; total he found was 12
Queen eats 1/5 leaving 4/5 = 12 ; total she found was 15
King eats 1/6 leaving 5/6 = 15 ; total king found was 18
2007-09-04 09:51:23 · answer #7 · answered by lenpol7 7 · 0⤊ 1⤋
In 40 days, the homeowner could paint 5 houses, and the painter could paint 8 houses. Thats 13 houses in 40 days together. So for just 1 house, it should be 40 / 13 days, or 3 and 1/13 days.
2016-04-03 03:33:22 · answer #8 · answered by Anonymous · 0⤊ 0⤋
originally there were 18 mangoes.
2007-09-04 09:41:31 · answer #9 · answered by icemoon 2 · 0⤊ 1⤋
b=a-a/6=5a/6
c=b-1/5b=4b/5
d=c-c/4=3c/4
e=d-d/3=2d/3
3=e-e/2=e/2
e/2=3
e=6
2d/3=6
d=9
3c/4=9
c=12
4b/5=12
b=15
5a/6=15
a=18
There were 18 mangoes.
2007-09-04 09:46:16 · answer #10 · answered by Larry C 3 · 0⤊ 0⤋