Distinction	Merit	Participation
Points awarded	8	6	2

Contestants in a quiz were awarded certificates based on their scores. A total of 800 points were awarded. ¹₃ of the contestants received the Distinction certificates. ²₇ of the remaining contestants received the Merit certificates and the rest received the Participation certificates. How many contestants received the Participation certificates?

Distinction	Merit	Participation
1x7	2x7
	2x2	5x2
7 u	4 u	10 u

	Distinction	Merit	Participation
Number	7 u	4 u	10 u
Value	8	6	2
Total value	56 u	24 u	20 u

The total number of contestants who received Merit certificates and Participation certificates is the combined repeated identity. LCM of 7 and 2 is 14.

Total points awarded
= 56 u + 24 u + 20 u
= 100 u

100 u = 800 

1 u = 800 ÷ 100 = 8

Number of contestants who received Participation certificates
= 10 u
= 10 x 8
= 80

Answer(s): 80