By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 9 students, find the number of handshakes.
- If there are 29 students, find the number of handshakes.
- If there are 276 handshakes, how many students are there?
(a)
Pattern for the number of handshakes
1 student: 0
2 students: 0 + 1 = 1
3 students: 0 + 1 + 2 = 3
4 students: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of students - 1) x (Number of students) ÷ 2
Number of handshakes for 9 students
= (9 - 1) x 9 ÷ 2
= 8 x 9 ÷ 2
= 36
(b)
Number of handshakes for 29 students
= (29 - 1) x 29 ÷ 2
= 28 x 29 ÷ 2
= 406
(c)
Guess & Check
276 = (Number of students - 1) x (Number of students) ÷ 2
276 x 2 = (Number of students - 1) x (Number of students)
552 = 23 x 24
Number of students = 24
Answer(s): (a) 36; (b) 406; (c) 24
