SOLUTION: Happy Hector and Party Paul are each having a catered party at Fun Factory. Hector�s party is in the hall and Paul�s party is on the Patio. The catering manager of Fun Factory expl

Question 71262: Happy Hector and Party Paul are each having a catered party at Fun Factory. Hector�s party is in the hall and Paul�s party is on the Patio. The catering manager of Fun Factory explained the rules to Hector and Paul. Both Hector�s party in the Hall and Paul�s party on the Patio must have the same size table, that is, for example, table size for 2,3,4,5,6,7,8,9, etc. The manager will only order one size table for both parties.He will order the largest size table possible. Everyone at each party must have a seat and no seats can be empty at any table. Hector will have a total of 180 people. Paul is expecting a total of 84 people. What is the largest-sized table the manager needs to order for both Hector and Paul?

Answer by sudhir(14) (Show Source): You can put this solution on YOUR website!
This looks to me to be a problem of Greatest Common Divisor( or some say Highest Common Factor)
look at both the parties the host wants all their guests to be seated.
and the manager tells them that table size should be same for both the parties.
but he did not put any restriction on the number of tables at any of the parties.
So, now the point is to find the maximum size of the table so that the size divides exactly the number of guests at both parties .
formula for finding HCF of two numbers say 'a' and 'b' is:-
HCF = (a*b)/(LCM of a and b)
see http://en.wikipedia.org/wiki/Greatest_common_diviso
here LCM of 84 and 180 = 1260
so, size of table = 84*180/1260
= 12 Answer.
RELATED QUESTIONS
Happy Hector and Party Paul are each having a catered party at Fun Factory. Hector�s... (answered by stanbon)

The cost p, in dollars, of having a dinner party catered by Elain's Kosher Catering... (answered by checkley77)

Sam and Tina are celebrating their 25th anniversary by having a party. They budgeted... (answered by htmentor)

Khang and Hector live 88 miles apart in southeastern Missouri. They decide to bicycle... (answered by lwsshak3,josmiceli)

Your family is planning a birthday party for you and is getting it catered . hamiltons... (answered by ikleyn)

In a party 68% of people who attend the party are man if 40% of man and 31.2 % of total... (answered by ankor@dixie-net.com)

every two persons shakes hand with each other in a party and the total number of hand... (answered by ikleyn)

Khang and Heator live 88 miles apart in southeastern Missouri. They decide to bicycle... (answered by richwmiller)

If at a party every person gives a gift to each other& total number of gift taken is 132. (answered by richwmiller)