By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 10 kids, find the number of handshakes.
- If there are 49 kids, find the number of handshakes.
- If there are 105 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 10 kids
= (10 - 1) x 10 ÷ 2
= 9 x 10 ÷ 2
= 45
(b)
Number of handshakes for 49 kids
= (49 - 1) x 49 ÷ 2
= 48 x 49 ÷ 2
= 1176
(c)
Guess & Check
105 = (Number of kids - 1) x (Number of kids) ÷ 2
105 x 2 = (Number of kids - 1) x (Number of kids)
210 = 14 x 15
Number of kids = 15
Answer(s): (a) 45; (b) 1176; (c) 15
