By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 5 men, find the number of handshakes.
- If there are 33 men, find the number of handshakes.
- If there are 66 handshakes, how many men are there?
(a)
Pattern for the number of handshakes
1 man: 0
2 men: 0 + 1 = 1
3 men: 0 + 1 + 2 = 3
4 men: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of men - 1) x (Number of men) ÷ 2
Number of handshakes for 5 men
= (5 - 1) x 5 ÷ 2
= 4 x 5 ÷ 2
= 10
(b)
Number of handshakes for 33 men
= (33 - 1) x 33 ÷ 2
= 32 x 33 ÷ 2
= 528
(c)
Guess & Check
66 = (Number of men - 1) x (Number of men) ÷ 2
66 x 2 = (Number of men - 1) x (Number of men)
132 = 11 x 12
Number of men = 12
Answer(s): (a) 10; (b) 528; (c) 12
