By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 6 men, find the number of handshakes.
- If there are 44 men, find the number of handshakes.
- If there are 120 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 6 men
= (6 - 1) x 6 ÷ 2
= 5 x 6 ÷ 2
= 15
(b)
Number of handshakes for 44 men
= (44 - 1) x 44 ÷ 2
= 43 x 44 ÷ 2
= 946
(c)
Guess & Check
120 = (Number of men - 1) x (Number of men) ÷ 2
120 x 2 = (Number of men - 1) x (Number of men)
240 = 15 x 16
Number of men = 16
Answer(s): (a) 15; (b) 946; (c) 16