By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 10 women, find the number of handshakes.
- If there are 41 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 10 women
= (10 - 1) x 10 ÷ 2
= 9 x 10 ÷ 2
= 45
(b)
Number of handshakes for 41 women
= (41 - 1) x 41 ÷ 2
= 40 x 41 ÷ 2
= 820
(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) 45; (b) 820; (c) 17
