| |
Distinction |
Merit |
Participation |
| Points awarded |
7 |
6 |
2 |
Students in a quiz were awarded certificates based on their scores. A total of 2470 points were awarded.
110 of the students received the Distinction certificates.
27 of the remaining students received the Merit certificates and the rest received the Participation certificates. How many students were there in the quiz?
| Distinction |
Merit |
Participation |
| 1x7 |
9x7 |
| |
2x9 |
5x9 |
| 7 u |
18 u |
45 u |
| |
Distinction |
Merit |
Participation |
| Number |
7 u |
18 u |
45 u |
| Value |
7 |
6 |
2 |
| Total value |
49 u |
108 u |
90 u |
The total number of students who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 7 and 9 is 63.
Total points awarded
= 49 u + 108 u + 90 u
= 247 u
247 u = 2470
1 u = 2470 ÷ 247 = 10
Number of students in the quiz
= 7 u + 18 u + 45 u
= 70 u
= 70 x 10
= 700
Answer(s): 700
