By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 7 students, find the number of handshakes.
- If there are 23 students, find the number of handshakes.
- If there are 105 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 7 students
= (7 - 1) x 7 ÷ 2
= 6 x 7 ÷ 2
= 21
(b)
Number of handshakes for 23 students
= (23 - 1) x 23 ÷ 2
= 22 x 23 ÷ 2
= 253
(c)
Guess & Check
105 = (Number of students - 1) x (Number of students) ÷ 2
105 x 2 = (Number of students - 1) x (Number of students)
210 = 14 x 15
Number of students = 15
Answer(s): (a) 21; (b) 253; (c) 15