By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 8 children, find the number of handshakes.
- If there are 37 children, find the number of handshakes.
- If there are 190 handshakes, how many children are there?
(a)
Pattern for the number of handshakes
1 child: 0
2 children: 0 + 1 = 1
3 children: 0 + 1 + 2 = 3
4 children: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of children - 1) x (Number of children) ÷ 2
Number of handshakes for 8 children
= (8 - 1) x 8 ÷ 2
= 7 x 8 ÷ 2
= 28
(b)
Number of handshakes for 37 children
= (37 - 1) x 37 ÷ 2
= 36 x 37 ÷ 2
= 666
(c)
Guess & Check
190 = (Number of children - 1) x (Number of children) ÷ 2
190 x 2 = (Number of children - 1) x (Number of children)
380 = 19 x 20
Number of children = 20
Answer(s): (a) 28; (b) 666; (c) 20