ska7945 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?
1. m+4/m(m-4)
2. 2m-4/m(m-4)
3. 4m-4/m(m-4)
4. 4m-8/m(m-4)
5. 4m-12/m(m-4)
I received a PM requesting that I solve this problem.
Let m=5, implying that there are 5 students.
Let each sandwich = 5 units, implying that 3 sandwiches = 3*5 = 15 units.
Since 3 sandwiches are distributed among all 5 students -- including Carol -- the number of units received by Carol from these 3 sandwiches = 15/5 = 3 units.
Since 4 of the 5 students do not share in the last sandwich, and Carol eats a portion of EVERY sandwich, all 5 units of the last sandwich must be given to Carol.
Thus, total units for Carol = 3+5 = 8 units.
Resulting fraction:
(Carol's units)/(units per sandwich) = 8/5. This is our target.
Now plug m=5 into the answer choices to see which yields our target of 8/5.
Each answer choice has the same denominator:
m(m-4) = 5(5-4) = 5.
To yield our target of 8/5, the correct answer choice must have a numerator of 8.
Only
E works:
4m-12 = (4*5) - 12 = 8.
The correct answer is
E.
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