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# Four extra-large sandwiches of exactly the same size were

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Manager
Joined: 28 Aug 2008
Posts: 98
Four extra-large sandwiches of exactly the same size were [#permalink]

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12 Sep 2008, 11:51
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Four extra-large sandwiches of exactly the same size were ordered for m students, where m>4 . Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich she ate would be what fraction of a whole extra-large sandwich?

m+4 / m(m-4)

2m-4 / m(m-4)

4m-4 / m(m-4)

4m-8 / m(m-4)

4m-12 / m(m-4)
Intern
Joined: 16 Jun 2008
Posts: 17
Location: Kiev, Ukraine

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12 Sep 2008, 12:31
Let's take a sandwich as 1. First we will talk about the first 3 sandwiches. Then the part of a sandwich which each student ate is 1/m where m is a number of students. It means that Carol ate 1/m of every first 3 sandwiches: 1/m*3=3/m.

Now let's look at the 4-th sandwich. As far as 4 students didn't eat it, so the part of a sandwich which each student ate is 1/(m-4). It means that Carol ate 1/(m-4) of the 4-th sandwich.

Totalle Carol ate 3/m+1/(m-4)=(3m-12+m)/m(m-4)=4m-12/m(m-4).
Re: PS ... Sandwiches   [#permalink] 12 Sep 2008, 12:31
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