By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 6 students, find the number of handshakes.
- If there are 26 students, find the number of handshakes.
- If there are 231 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 6 students
= (6 - 1) x 6 ÷ 2
= 5 x 6 ÷ 2
= 15
(b)
Number of handshakes for 26 students
= (26 - 1) x 26 ÷ 2
= 25 x 26 ÷ 2
= 325
(c)
Guess & Check
231 = (Number of students - 1) x (Number of students) ÷ 2
231 x 2 = (Number of students - 1) x (Number of students)
462 = 21 x 22
Number of students = 22
Answer(s): (a) 15; (b) 325; (c) 22