By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 9 women, find the number of handshakes.
- If there are 32 women, find the number of handshakes.
- If there are 210 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 9 women
= (9 - 1) x 9 ÷ 2
= 8 x 9 ÷ 2
= 36
(b)
Number of handshakes for 32 women
= (32 - 1) x 32 ÷ 2
= 31 x 32 ÷ 2
= 496
(c)
Guess & Check
210 = (Number of women - 1) x (Number of women) ÷ 2
210 x 2 = (Number of women - 1) x (Number of women)
420 = 20 x 21
Number of women = 21
Answer(s): (a) 36; (b) 496; (c) 21
