Distinction	Merit	Participation
Points awarded	8	5	3

Participants in a quiz were awarded certificates based on their scores. A total of 327 points were awarded. ¹₄ of the participants received the Distinction certificates. ⁴₅ of the remaining participants received the Merit certificates and the rest received the Participation certificates. How many participants received the Distinction certificates?

Distinction	Merit	Participation
1x5	3x5
	4x3	1x3
5 u	12 u	3 u

	Distinction	Merit	Participation
Number	5 u	12 u	3 u
Value	8	5	3
Total value	40 u	60 u	9 u

The total number of participants who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 5 and 3 is 15.

Total points awarded
= 40 u + 60 u + 9 u
= 109 u

109 u = 327 u

1 u = 327 ÷ 109 = 3

Number of participants who received Distinction certificates
= 5 u
= 5 x 3
= 15

Answer(s): 15