At a race, ²₃ of the number of boys is equal to ¹₃ of the number of girls. The number of adults at the race is five times the number of children. The number of coupons given to each adult, boy and girl at the race is 6, 5 and 4 respectively. The total number of coupons given at the race is 2163.

1. What is the total number of coupons given to the adults?
2. What is the number of girls at the race?

(a)
Make the numerators the same.
²₃ of the boys = ¹₃ of the girls
²₃ of the boys = ²₆ of the girls

	Boys	Girls	Adults
Number	3 u	6 u	45 u
Value	5	4	6
Total value	15 u	24 u	270 u

Number of children
= 3 u + 6 u
= 9 u

Number of adults
= 5 x 9 u 
= 45 u

Total number of coupons given at the race
= 15 u + 24 u + 270 u
= 309 u

309 u = 2163

1 u = 2163 ÷ 309 = 7

Total number of coupons given to adults
= 270 u
= 270 x 7
= 1890

(b)
Number of girls in the race
= 6 u
= 6 x 7
= 42

Answer(s): (a) 1890; (b) 42