At a race, ²₅ of the number of women is equal to ¹₅ of the number of men. The number of children at the race is four times the number of adults. The number of coupons given to each child, woman and man at the race is 3, 2 and 1 respectively. The total number of coupons given at the race is 1400.

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.
²₅ of the women = ¹₅ of the men
²₅ of the women = ²₁₀ of the men

	Women	Men	Children
Number	5 u	10 u	60 u
Value	2	1	3
Total value	10 u	10 u	180 u

Number of adults
= 5 u + 10 u
= 15 u

Number of children
= 4 x 15 u 
= 60 u

Total number of coupons given at the race
= 10 u + 10 u + 180 u
= 200 u

200 u = 1400

1 u = 1400 ÷ 200 = 7

Total number of coupons given to children
= 180 u
= 180 x 7
= 1260

(b)
Number of men in the race
= 10 u
= 10 x 7
= 70

Answer(s): (a) 1260; (b) 70