By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 5 kids, find the number of handshakes.
- If there are 48 kids, find the number of handshakes.
- If there are 136 handshakes, how many kids are there?
(a)
Pattern for the number of handshakes
1 kid: 0
2 kids: 0 + 1 = 1
3 kids: 0 + 1 + 2 = 3
4 kids: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of kids - 1) x (Number of kids) ÷ 2
Number of handshakes for 5 kids
= (5 - 1) x 5 ÷ 2
= 4 x 5 ÷ 2
= 10
(b)
Number of handshakes for 48 kids
= (48 - 1) x 48 ÷ 2
= 47 x 48 ÷ 2
= 1128
(c)
Guess & Check
136 = (Number of kids - 1) x (Number of kids) ÷ 2
136 x 2 = (Number of kids - 1) x (Number of kids)
272 = 16 x 17
Number of kids = 17
Answer(s): (a) 10; (b) 1128; (c) 17