By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 5 women, find the number of handshakes.
- If there are 22 women, find the number of handshakes.
- If there are 190 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 5 women
= (5 - 1) x 5 ÷ 2
= 4 x 5 ÷ 2
= 10
(b)
Number of handshakes for 22 women
= (22 - 1) x 22 ÷ 2
= 21 x 22 ÷ 2
= 231
(c)
Guess & Check
190 = (Number of women - 1) x (Number of women) ÷ 2
190 x 2 = (Number of women - 1) x (Number of women)
380 = 19 x 20
Number of women = 20
Answer(s): (a) 10; (b) 231; (c) 20