By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 7 men, find the number of handshakes.
- If there are 48 men, find the number of handshakes.
- If there are 300 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 7 men
= (7 - 1) x 7 ÷ 2
= 6 x 7 ÷ 2
= 21
(b)
Number of handshakes for 48 men
= (48 - 1) x 48 ÷ 2
= 47 x 48 ÷ 2
= 1128
(c)
Guess & Check
300 = (Number of men - 1) x (Number of men) ÷ 2
300 x 2 = (Number of men - 1) x (Number of men)
600 = 24 x 25
Number of men = 25
Answer(s): (a) 21; (b) 1128; (c) 25