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 33 women, find the number of handshakes.
- If there are 276 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 33 women
= (33 - 1) x 33 ÷ 2
= 32 x 33 ÷ 2
= 528
(c)
Guess & Check
276 = (Number of women - 1) x (Number of women) ÷ 2
276 x 2 = (Number of women - 1) x (Number of women)
552 = 23 x 24
Number of women = 24
Answer(s): (a) 15; (b) 528; (c) 24