At a race, ¹₃ of the number of women is equal to ²₇ of the number of men. The number of children at the race is five times the number of adults. The number of coupons given to each child, woman and man at the race is 4, 3 and 2 respectively. The total number of coupons given at the race is 584.

1. What is the total number of coupons given to the children?
2. What is the number of men at the race?

(a)
Make the numerators the same.
¹₃ of the women = ²₇ of the men
²₆ of the women = ²₇ of the men

	Women	Men	Children
Number	6 u	7 u	65 u
Value	3	2	4
Total value	18 u	14 u	260 u

Number of adults
= 6 u + 7 u
= 13 u

Number of children
= 5 x 13 u 
= 65 u

Total number of coupons given at the race
= 18 u + 14 u + 260 u
= 292 u

292 u = 584

1 u = 584 ÷ 292 = 2

Total number of coupons given to children
= 260 u
= 260 x 2
= 520

(b)
Number of men in the race
= 7 u
= 7 x 2
= 14

Answer(s): (a) 520; (b) 14