| |
Distinction |
Merit |
Participation |
| Points awarded |
7 |
5 |
2 |
Contestants in a quiz were awarded certificates based on their scores. A total of 699 points were awarded.
311 of the contestants received the Distinction certificates.
25 of the remaining contestants received the Merit certificates and the rest received the Participation certificates. How many contestants were there in the quiz?
| Distinction |
Merit |
Participation |
| 3x5 |
8x5 |
| |
2x8 |
3x8 |
| 15 u |
16 u |
24 u |
| |
Distinction |
Merit |
Participation |
| Number |
15 u |
16 u |
24 u |
| Value |
7 |
5 |
2 |
| Total value |
105 u |
80 u |
48 u |
The total number of contestants who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 5 and 8 is 40.
Total points awarded
= 105 u + 80 u + 48 u
= 233 u
233 u = 699
1 u = 699 ÷ 233 = 3
Number of contestants in the quiz
= 15 u + 16 u + 24 u
= 55 u
= 55 x 3
= 165
Answer(s): 165
