By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 5 guests, find the number of handshakes.
- If there are 47 guests, find the number of handshakes.
- If there are 171 handshakes, how many guests are there?
(a)
Pattern for the number of handshakes
1 guest: 0
2 guests: 0 + 1 = 1
3 guests: 0 + 1 + 2 = 3
4 guests: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of guests - 1) x (Number of guests) ÷ 2
Number of handshakes for 5 guests
= (5 - 1) x 5 ÷ 2
= 4 x 5 ÷ 2
= 10
(b)
Number of handshakes for 47 guests
= (47 - 1) x 47 ÷ 2
= 46 x 47 ÷ 2
= 1081
(c)
Guess & Check
171 = (Number of guests - 1) x (Number of guests) ÷ 2
171 x 2 = (Number of guests - 1) x (Number of guests)
342 = 18 x 19
Number of guests = 19
Answer(s): (a) 10; (b) 1081; (c) 19
