|
Distinction |
Merit |
Participation |
Points awarded |
10 |
5 |
3 |
Participants in a quiz were awarded certificates based on their scores. A total of 3179 points were awarded.
211 of the participants received the Distinction certificates.
35 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 |
2x5 |
9x5 |
|
3x9 |
2x9 |
10 u |
27 u |
18 u |
|
Distinction |
Merit |
Participation |
Number |
10 u |
27 u |
18 u |
Value |
10 |
5 |
3 |
Total value |
100 u |
135 u |
54 u |
The total number of participants who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 5 and 9 is 45.
Total points awarded
= 100 u + 135 u + 54 u
= 289 u
289 u = 3179
1 u = 3179 ÷ 289 = 11
Number of participants in the quiz
= 10 u + 27 u + 18 u
= 55 u
= 55 x 11
= 605
Answer(s): 605