By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 6 women, find the number of handshakes.
- If there are 37 women, find the number of handshakes.
- If there are 105 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 6 women
= (6 - 1) x 6 ÷ 2
= 5 x 6 ÷ 2
= 15
(b)
Number of handshakes for 37 women
= (37 - 1) x 37 ÷ 2
= 36 x 37 ÷ 2
= 666
(c)
Guess & Check
105 = (Number of women - 1) x (Number of women) ÷ 2
105 x 2 = (Number of women - 1) x (Number of women)
210 = 14 x 15
Number of women = 15
Answer(s): (a) 15; (b) 666; (c) 15