By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 7 kids, find the number of handshakes.
- If there are 25 kids, find the number of handshakes.
- If there are 190 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 7 kids
= (7 - 1) x 7 ÷ 2
= 6 x 7 ÷ 2
= 21
(b)
Number of handshakes for 25 kids
= (25 - 1) x 25 ÷ 2
= 24 x 25 ÷ 2
= 300
(c)
Guess & Check
190 = (Number of kids - 1) x (Number of kids) ÷ 2
190 x 2 = (Number of kids - 1) x (Number of kids)
380 = 19 x 20
Number of kids = 20
Answer(s): (a) 21; (b) 300; (c) 20