| |
Distinction |
Merit |
Participation |
| Points awarded |
9 |
5 |
3 |
Children in a quiz were awarded certificates based on their scores. A total of 2230 points were awarded.
29 of the children received the Distinction certificates.
25 of the remaining children received the Merit certificates and the rest received the Participation certificates. How many children were there in the quiz?
| Distinction |
Merit |
Participation |
| 2x5 |
7x5 |
| |
2x7 |
3x7 |
| 10 u |
14 u |
21 u |
| |
Distinction |
Merit |
Participation |
| Number |
10 u |
14 u |
21 u |
| Value |
9 |
5 |
3 |
| Total value |
90 u |
70 u |
63 u |
The total number of children who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 5 and 7 is 35.
Total points awarded
= 90 u + 70 u + 63 u
= 223 u
223 u = 2230
1 u = 2230 ÷ 223 = 10
Number of children in the quiz
= 10 u + 14 u + 21 u
= 45 u
= 45 x 10
= 450
Answer(s): 450
