At a race, ¹₅ of the number of girls is equal to ²₃ of the number of boys. The number of adults at the race is five times the number of children. The number of coupons given to each adult, girl and boy at the race is 3, 2 and 1 respectively. The total number of coupons given at the race is 2398.

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

(a)
Make the numerators the same.
¹₅ of the girls = ²₃ of the boys
²₁₀ of the girls = ²₃ of the boys

	Girls	Boys	Adults
Number	10 u	3 u	65 u
Value	2	1	3
Total value	20 u	3 u	195 u

Number of children
= 10 u + 3 u
= 13 u

Number of adults
= 5 x 13 u 
= 65 u

Total number of coupons given at the race
= 20 u + 3 u + 195 u
= 218 u

218 u = 2398

1 u = 2398 ÷ 218 = 11

Total number of coupons given to adults
= 195 u
= 195 x 11
= 2145

(b)
Number of boys in the race
= 3 u
= 3 x 11
= 33

Answer(s): (a) 2145; (b) 33