A cater is planning a large dinner party for 455 guest each table must take an equal number of guest more than one guest and fewer than 20 determine the number of possible table sizes. If the cater uses 7 person tables how many tables will they need?
Total guest =455
Guest on each table =x. 1<x<20
455= 5×7×13
Member= 5;7;13
Table required=7×13=91( 5 member);65(7 member); 35 (13 member)
Possible table size =3
For 7 member=65
To determine the number of possible table sizes for the dinner party, we need to find the numbers between 1 and 19 that are divisible by the number of guests per table.
Since each table must take an equal number of guests more than one and fewer than twenty, we can start by finding the divisors of the number of guests per table, which is 7 in this case.
The divisors of 7 are 1 and 7 itself. Therefore, the possible table sizes are 1 table and 7 tables.
Next, to determine the number of tables needed, we divide the total number of guests (455) by the number of guests per table (7).
455 ÷ 7 = 65.
So, the caterer will need 65 tables.
In summary, there are 2 possible table sizes (1 table and 7 tables), and the caterer will need 65 tables for the dinner party.