| |
Distinction |
Merit |
Participation |
| Points awarded |
8 |
4 |
1 |
Pupils in a quiz were awarded certificates based on their scores. A total of 360 points were awarded.
15 of the pupils received the Distinction certificates.
37 of the remaining pupils received the Merit certificates and the rest received the Participation certificates. How many pupils were there in the quiz?
| Distinction |
Merit |
Participation |
| 1x7 |
4x7 |
| |
3x4 |
4x4 |
| 7 u |
12 u |
16 u |
| |
Distinction |
Merit |
Participation |
| Number |
7 u |
12 u |
16 u |
| Value |
8 |
4 |
1 |
| Total value |
56 u |
48 u |
16 u |
The total number of pupils who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 7 and 4 is 28.
Total points awarded
= 56 u + 48 u + 16 u
= 120 u
120 u = 360
1 u = 360 ÷ 120 = 3
Number of pupils in the quiz
= 7 u + 12 u + 16 u
= 35 u
= 35 x 3
= 105
Answer(s): 105
