By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 7 guests, find the number of handshakes.
- If there are 32 guests, find the number of handshakes.
- If there are 276 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 7 guests
= (7 - 1) x 7 ÷ 2
= 6 x 7 ÷ 2
= 21
(b)
Number of handshakes for 32 guests
= (32 - 1) x 32 ÷ 2
= 31 x 32 ÷ 2
= 496
(c)
Guess & Check
276 = (Number of guests - 1) x (Number of guests) ÷ 2
276 x 2 = (Number of guests - 1) x (Number of guests)
552 = 23 x 24
Number of guests = 24
Answer(s): (a) 21; (b) 496; (c) 24
