Peter, Paul and you decided to divide some marbles among yourselves........

Question

shubhamsrg · Answer

nop, i am not gonna share my marbles

anonymous · Answer

Peter, paul and you decided to divide some marbles among yourselves. Suppose you got half of the marbles and one more. If Peter took one more then half of those left, and Paul had 8 remaining marbles, how many marbles were there originally ?

anonymous · Answer

Please help me set this up......my mind just isn't working very good right now...lol

ganeshie8 · Answer

$\large  m - \frac{(\frac{1}{2} m + 1)}{2} + 1 = 8$

anonymous · Answer

do I multiply everything by 2 ?

ganeshie8 · Answer

wait ive just put something, lets see if it fits the given data or not lol

ganeshie8 · Answer

say, total number of marbles = m

ganeshie8 · Answer

I got half of marbles and 1 more :-

$\frac{1}{2}m + 1$

anonymous · Answer

ok......"you' has got 1/2m + 1....

anonymous · Answer

and Paul has 8

ganeshie8 · Answer

after ive taken half +1, remaining marbles  = 

$m  - (\frac{1}{2}m+1)$

ganeshie8 · Answer

from this remaining, peter took half + 1 more, so

Peter has : $\frac{m-(\frac{1}{2}m+1)}{2} + 1$

anonymous · Answer

oh....I see

ganeshie8 · Answer

whats left is 8, so :-

ganeshie8 · Answer

$m - ME - PETER = 8$

anonymous · Answer

m - (1/2m + 1)/(2 ) + 1 = 8.....

anonymous · Answer

do I multiply everything by 2 to get rid of the fraction ?

ganeshie8 · Answer

$m - (\frac{1}{2}m + 1)  - (\frac{m-(\frac{1}{2}m+1)}{2}+1) = 8$

ganeshie8 · Answer

solve m, yes multiply everything with 2 and see

anonymous · Answer

2m - (m + 1) - 2m - m + 1 = 16
amI doing this right ?

ganeshie8 · Answer

$m - (\frac{1}{2}m + 1)  - (\frac{m-(\frac{1}{2}m+1)}{2}+1) = 8 $

$2m - (m+2)  - (m-(\frac{1}{2}m+1)+2) = 16 $

ganeshie8 · Answer

simplify a bit

ganeshie8 · Answer

$m - (\frac{1}{2}m + 1)  - (\frac{m-(\frac{1}{2}m+1)}{2}+1) = 8 $

$2m - (m+2)  - (m-(\frac{1}{2}m+1)+2) = 16 $

$2m - m-2  - m+(\frac{1}{2}m+1)-2 = 16 $

$-4  + (\frac{1}{2}m+1) = 16 $

anonymous · Answer

-4 + 1/2m + 1 = 16
1/2m = 16 + 4 - 1
1/2m = 19
m = 8
Is that correct ?

ganeshie8 · Answer

you mean m = 38 ?

anonymous · Answer

oh...oops...your right.....
so " you " then has:
1/2m + 1 = 1/2(38) + 1 = 19 + 1 = 20

Peter has : (m - 1/2m + 1)/(2) + 1 =
 (38 - 1/2(38) + 1)/2
(38 - 19 + 1)/2 = 20/2 = 10

peter has 8

check....
20 + 10 + 8 = 38

OMG...your good

ganeshie8 · Answer

nope, you're really good :) good work !!

anonymous · Answer

oops paul has 8 not peter ......thank you so much for your help

ganeshie8 · Answer

you're wlcme :D