Question 853428: a caterer is planning a large dinner party for 1001 guests. Each table must seat and equal number of guests, more than 1 guest and fewer than 20. Determine the number of possible table sizes. If the caterers use 7 person tables, how many tables will they need?
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! If there are 7 people per table, simply divide 1001/7 to get 143 tables.
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For the others, the key is here: Each table must seat and equal number of guests
So only table seatings that evenly go into 1001 can be considered. Which numbers 2-19 are factors of 1001? 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
We can immediately toss the even ones. 3,5,7,9,11,13,15,17,19
We know that 5's don't fit. 3,7,9,11,13,17,19
Divide 1001 by the numbers to find the possibilities where there is no remainder: 7, 11, 13
Those are the only 3 table sizes that work.
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