By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 8 women, find the number of handshakes.
- If there are 21 women, find the number of handshakes.
- If there are 136 handshakes, how many women are there?
(a)
Pattern for the number of handshakes
1 woman: 0
2 women: 0 + 1 = 1
3 women: 0 + 1 + 2 = 3
4 women: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of women - 1) x (Number of women) ÷ 2
Number of handshakes for 8 women
= (8 - 1) x 8 ÷ 2
= 7 x 8 ÷ 2
= 28
(b)
Number of handshakes for 21 women
= (21 - 1) x 21 ÷ 2
= 20 x 21 ÷ 2
= 210
(c)
Guess & Check
136 = (Number of women - 1) x (Number of women) ÷ 2
136 x 2 = (Number of women - 1) x (Number of women)
272 = 16 x 17
Number of women = 17
Answer(s): (a) 28; (b) 210; (c) 17
