By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 10 adults, find the number of handshakes.
- If there are 50 adults, find the number of handshakes.
- If there are 171 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 10 adults
= (10 - 1) x 10 ÷ 2
= 9 x 10 ÷ 2
= 45
(b)
Number of handshakes for 50 adults
= (50 - 1) x 50 ÷ 2
= 49 x 50 ÷ 2
= 1225
(c)
Guess & Check
171 = (Number of adults - 1) x (Number of adults) ÷ 2
171 x 2 = (Number of adults - 1) x (Number of adults)
342 = 18 x 19
Number of adults = 19
Answer(s): (a) 45; (b) 1225; (c) 19
