A caterer is planning a large party for 231 guest. Each table must seat an equal number of guest , more than 1 guest and fewer than 20. Determine the number of possible table sizes. If the caterers use 11 persons tables, how many tables will they need?
there are blank possibles tables sizes that will give equal number of guest more than 1 guest and fewerer than 20?
231/11 = 21 tables
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To determine the number of possible table sizes that can seat an equal number of guests, more than 1 guest, and fewer than 20, we need to find the factors of 231 that satisfy these conditions.
First, let's factorize 231:
231 = 1 x 231
= 3 x 77
= 7 x 33
Now, let's check each factor to see if it meets the given conditions.
For 1 guest: 1 is not greater than 1, so it doesn't satisfy the conditions.
For 3 guests: 3 is an acceptable table size.
For 7 guests: 7 is an acceptable table size.
For 11 guests: 11 is an acceptable table size.
For 33 guests: 33 is not less than 20, so it doesn't satisfy the conditions.
For 77 guests: 77 is not less than 20, so it doesn't satisfy the conditions.
For 231 guests: 231 is not less than 20, so it doesn't satisfy the conditions.
Therefore, the possible table sizes that meet the given conditions are 3, 7, and 11.
Now, let's calculate how many tables will be needed if the caterers use 11-person tables.
To determine the number of tables needed, we divide the total number of guests (231) by the number of guests per table (11):
Number of tables = Total number of guests / Guests per table
= 231 / 11
= 21
Therefore, the caterers will need 21 tables if they use 11-person tables.