By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 6 adults, find the number of handshakes.
- If there are 21 adults, find the number of handshakes.
- If there are 105 handshakes, how many adults are there?
(a)
Pattern for the number of handshakes
1 adult: 0
2 adults: 0 + 1 = 1
3 adults: 0 + 1 + 2 = 3
4 adults: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of adults - 1) x (Number of adults) ÷ 2
Number of handshakes for 6 adults
= (6 - 1) x 6 ÷ 2
= 5 x 6 ÷ 2
= 15
(b)
Number of handshakes for 21 adults
= (21 - 1) x 21 ÷ 2
= 20 x 21 ÷ 2
= 210
(c)
Guess & Check
105 = (Number of adults - 1) x (Number of adults) ÷ 2
105 x 2 = (Number of adults - 1) x (Number of adults)
210 = 14 x 15
Number of adults = 15
Answer(s): (a) 15; (b) 210; (c) 15