Problem Solving

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 that she ate would be what fraction of a whole extra-large sandwich?


A. m+4/m(m-4) B. 2m-4/m(m-4) C.4m-4/m(m-4) D. 4m-8/m(m-4)
E. 4m-12/m(m-4)


I tried to plug in the number (assume that m=12) ...can't get the right answer.

First 3 sandwiches divided amongst m people, so each person gets 3/m
of the sandwich.

Last sandwich divided among m-4. So each person gets 1/(m-4)

So carol eats 3/m + 1/(m-4) = (4m-12) / (m(m-4))

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 that she ate would be what fraction of a whole extra-large sandwich?


A. m+4/m(m-4)
B. 2m-4/m(m-4)
C.4m-4/m(m-4)
D. 4m-8/m(m-4)
E. 4m-12/m(m-4)


This one seems easy...Lets hope I get it right

First 3 sandwiches divided amongst m students

Thus each student gets 3/m sandwich

Last sandwich divided amongst m - 4 students

Therefore each of those m-4 students gets 1/m-4 sandwich

Carol ate 3/m + 1/m-4 sandwich

= (3(m-4)+m)/m(m-4)

= 3m - 12 + m / m (m - 4)

= 4m - 12 / m (m - 4)

Hence E

Value substitution and algebra both work nicely for this question. See videos below:

Value substitution: https://youtu.be/L-fqOMzmglM

Algebra: https://youtu.be/usxNJ89lAZs

Hope they help.

metropia wrote: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 that she ate would be what fraction of a whole extra-large sandwich?


A. m+4/m(m-4) B. 2m-4/m(m-4) C.4m-4/m(m-4) D. 4m-8/m(m-4)
E. 4m-12/m(m-4)


I tried to plug in the number (assume that m=12) ...can't get the right answer.

Instead of number substituting, simple algebra would get you the answer quickly

3 sandwiches divided among m students.
Hence each student gets 3/m sandwiches

For the last one, 4 students do not want to eat, hence remaining students = m - 4
Each student gets 1/ (m-4) sandwiches

Total sandwiches eaten by Carol = 3/m + 1/(m-4) = 3m - 12 + m / m(m-4) = 4m-12/m(m-4)

Correct Option: E

Since the OP asked the question in 2007, I think we can assume the sandwiches are long spoiled, and there's no need to resurrect the thread.