By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 5 students, find the number of handshakes.
- If there are 39 students, find the number of handshakes.
- If there are 171 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 5 students
= (5 - 1) x 5 ÷ 2
= 4 x 5 ÷ 2
= 10
(b)
Number of handshakes for 39 students
= (39 - 1) x 39 ÷ 2
= 38 x 39 ÷ 2
= 741
(c)
Guess & Check
171 = (Number of students - 1) x (Number of students) ÷ 2
171 x 2 = (Number of students - 1) x (Number of students)
342 = 18 x 19
Number of students = 19
Answer(s): (a) 10; (b) 741; (c) 19
