|
Distinction |
Merit |
Participation |
Points awarded |
10 |
6 |
3 |
Contestants in a quiz were awarded certificates based on their scores. A total of 126 points were awarded.
14 of the contestants received the Distinction certificates.
29 of the remaining contestants received the Merit certificates and the rest received the Participation certificates. How many contestants received the Distinction certificates?
Distinction |
Merit |
Participation |
1x3 |
3x3 |
|
2x1 |
7x1 |
3 u |
2 u |
7 u |
|
Distinction |
Merit |
Participation |
Number |
3 u |
2 u |
7 u |
Value |
10 |
6 |
3 |
Total value |
30 u |
12 u |
21 u |
The total number of contestants who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 9 and 3 is 9.
Total points awarded
= 30 u + 12 u + 21 u
= 63 u
63 u = 126 u
1 u = 126 ÷ 63 = 2
Number of contestants who received Distinction certificates
= 3 u
= 3 x 2
= 6
Answer(s): 6