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If Sam has 5 more marbles than Jack, Jack has 4 more marbles

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VP
Joined: 18 May 2008
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If Sam has 5 more marbles than Jack, Jack has 4 more marbles [#permalink]  31 May 2008, 04:15
If Sam has 5 more marbles than Jack, Jack has 4 more marbles than Frank, and Frank has 5 more marbles than Ted, what is the least number of marbles that must change hands if the four boys are to have an equal number of marbles?

1. 7
2. 8
3. 9
4. 14
5. 28
Manager
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Re: Algebra [#permalink]  31 May 2008, 05:27
ritula wrote:
If Sam has 5 more marbles than Jack, Jack has 4 more marbles than Frank, and Frank has 5 more marbles than Ted, what is the least number of marbles that must change hands if the four boys are to have an equal number of marbles?

1. 7
2. 8
3. 9
4. 14
5. 28

lets arrange al in terms of sam and the comparing the numbers of marbles each has more that the person who has least

sam=s marbles= 14 more

jack=s-5=9 more

frank =s-9=5 more

ted=s-14=0 more

so shift 5 from sam to ted =shift =5

sam and jack have 9 more shift 2 from then to the other -shifts=4
total shifts=9 and each has 7
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Re: Algebra [#permalink]  31 May 2008, 05:31
Ted = x
Frank = x + 5
Jack = x + 9
Sam = x + 14

14 + 9 + 5 = 28
28/4 = 7

So Each one of them should have x + 7 marbles.

Move 2 Marbles from Jack to Frank.
Move 7 marbles from Sam to Ted.

Ted = x + 7
Frank = x + 7
Jack = x + 7
Sam = x + 7

Marbles moved = 2 + 7 = 9

VP
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Re: Algebra [#permalink]  31 May 2008, 05:38
Thanks ! Nice explanation
Manager
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Re: Algebra [#permalink]  31 May 2008, 05:39
ritula wrote:
If Sam has 5 more marbles than Jack, Jack has 4 more marbles than Frank, and Frank has 5 more marbles than Ted, what is the least number of marbles that must change hands if the four boys are to have an equal number of marbles?

1. 7
2. 8
3. 9
4. 14
5. 28

from the question
S=J+5
J=F+4
F=T+5

lets assume ted has 5 marbles
we can find
F=10
J=14
S=19

Total marbles=48
which means every guy should gt 12 each
We take 7 from sam and 2 from jack
Thats a total of 9
I found it to be an easier way !

Cheers
Re: Algebra   [#permalink] 31 May 2008, 05:39
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