By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 9 adults, find the number of handshakes.
- If there are 28 adults, find the number of handshakes.
- If there are 210 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 9 adults
= (9 - 1) x 9 ÷ 2
= 8 x 9 ÷ 2
= 36
(b)
Number of handshakes for 28 adults
= (28 - 1) x 28 ÷ 2
= 27 x 28 ÷ 2
= 378
(c)
Guess & Check
210 = (Number of adults - 1) x (Number of adults) ÷ 2
210 x 2 = (Number of adults - 1) x (Number of adults)
420 = 20 x 21
Number of adults = 21
Answer(s): (a) 36; (b) 378; (c) 21