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 30 men, find the number of handshakes.
- If there are 136 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 30 men
= (30 - 1) x 30 ÷ 2
= 29 x 30 ÷ 2
= 435
(c)
Guess & Check
136 = (Number of men - 1) x (Number of men) ÷ 2
136 x 2 = (Number of men - 1) x (Number of men)
272 = 16 x 17
Number of men = 17
Answer(s): (a) 10; (b) 435; (c) 17