At a race, ⁴₅ of the number of men is equal to ¹₆ of the number of women. The number of children at the race is four times the number of adults. The number of coupons given to each child, man and woman at the race is 7, 6 and 5 respectively. The total number of coupons given at the race is 7696.

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

(a)
Make the numerators the same.
⁴₅ of the men = ¹₆ of the women
⁴₅ of the men = ⁴₂₄ of the women

	Men	Women	Children
Number	5 u	24 u	116 u
Value	6	5	7
Total value	30 u	120 u	812 u

Number of adults
= 5 u + 24 u
= 29 u

Number of children
= 4 x 29 u 
= 116 u

Total number of coupons given at the race
= 30 u + 120 u + 812 u
= 962 u

962 u = 7696

1 u = 7696 ÷ 962 = 8

Total number of coupons given to children
= 812 u
= 812 x 8
= 6496

(b)
Number of women in the race
= 24 u
= 24 x 8
= 192

Answer(s): (a) 6496; (b) 192