By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 9 guests, find the number of handshakes.
- If there are 37 guests, find the number of handshakes.
- If there are 91 handshakes, how many guests are there?
(a)
Pattern for the number of handshakes
1 guest: 0
2 guests: 0 + 1 = 1
3 guests: 0 + 1 + 2 = 3
4 guests: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of guests - 1) x (Number of guests) ÷ 2
Number of handshakes for 9 guests
= (9 - 1) x 9 ÷ 2
= 8 x 9 ÷ 2
= 36
(b)
Number of handshakes for 37 guests
= (37 - 1) x 37 ÷ 2
= 36 x 37 ÷ 2
= 666
(c)
Guess & Check
91 = (Number of guests - 1) x (Number of guests) ÷ 2
91 x 2 = (Number of guests - 1) x (Number of guests)
182 = 13 x 14
Number of guests = 14
Answer(s): (a) 36; (b) 666; (c) 14