By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 5 adults, find the number of handshakes.
- If there are 41 adults, find the number of handshakes.
- If there are 91 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 5 adults
= (5 - 1) x 5 ÷ 2
= 4 x 5 ÷ 2
= 10
(b)
Number of handshakes for 41 adults
= (41 - 1) x 41 ÷ 2
= 40 x 41 ÷ 2
= 820
(c)
Guess & Check
91 = (Number of adults - 1) x (Number of adults) ÷ 2
91 x 2 = (Number of adults - 1) x (Number of adults)
182 = 13 x 14
Number of adults = 14
Answer(s): (a) 10; (b) 820; (c) 14