|
Distinction |
Merit |
Participation |
Points awarded |
10 |
5 |
2 |
Participants in a quiz were awarded certificates based on their scores. A total of 168 points were awarded.
111 of the participants received the Distinction certificates.
25 of the remaining participants received the Merit certificates and the rest received the Participation certificates. How many participants were there in the quiz?
Distinction |
Merit |
Participation |
1x1 |
10x1 |
|
2x2 |
3x2 |
1 u |
4 u |
6 u |
|
Distinction |
Merit |
Participation |
Number |
1 u |
4 u |
6 u |
Value |
10 |
5 |
2 |
Total value |
10 u |
20 u |
12 u |
The total number of participants who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 5 and 10 is 10.
Total points awarded
= 10 u + 20 u + 12 u
= 42 u
42 u = 168
1 u = 168 ÷ 42 = 4
Number of participants in the quiz
= 1 u + 4 u + 6 u
= 11 u
= 11 x 4
= 44
Answer(s): 44