By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 6 kids, find the number of handshakes.
- If there are 42 kids, find the number of handshakes.
- If there are 300 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 6 kids
= (6 - 1) x 6 ÷ 2
= 5 x 6 ÷ 2
= 15
(b)
Number of handshakes for 42 kids
= (42 - 1) x 42 ÷ 2
= 41 x 42 ÷ 2
= 861
(c)
Guess & Check
300 = (Number of kids - 1) x (Number of kids) ÷ 2
300 x 2 = (Number of kids - 1) x (Number of kids)
600 = 24 x 25
Number of kids = 25
Answer(s): (a) 15; (b) 861; (c) 25