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 50 women, find the number of handshakes.
- If there are 253 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 50 women
= (50 - 1) x 50 ÷ 2
= 49 x 50 ÷ 2
= 1225
(c)
Guess & Check
253 = (Number of women - 1) x (Number of women) ÷ 2
253 x 2 = (Number of women - 1) x (Number of women)
506 = 22 x 23
Number of women = 23
Answer(s): (a) 45; (b) 1225; (c) 23
