PSLE
The number of girls and boys taking part in a contest are in the ratio 6 : 7. These students are put into two teams. 40% of the girls and 30% of the boys are in Team Y. The rest of the students are in Team Z.

1. What is the ratio of the number of students in Team Z to Team Y? Give your answer in the simplest form.
2. The number of boys in Team Y is more than 90. What is the smallest possible total number of students taking part in the contest?

Girls		Boys
60 u		70 u
Team Y	Team Z	Team Y	Team Z
24 u	36 u	21 u	49 u

(a)
Girls : Boys
6 : 7
60 : 70

Number of girls in Team Y
= 40% x 60 u
= ⁴⁰₁₀₀ x 60 u
= 24 u

Number of girls in Team Z
= 60 u - 24 u
= 36 u

Number of boys in Team Y
= 30% x 70 u
= ³⁰₁₀₀ x 70 u
= 21 u

Number of boys in Team Z
= 70 u - 21 u
= 49 u

Team Y : Team Z
36 + 49 : 24 + 21 
85 : 45 _(÷5)
17 : 9

(b)
Number of boys in Team Y = 21 u

Since the number of boys in Team Y is 21 u, it must be multiple of 21.

Number of sets of 21
= 90 ÷ 21
= 4 r 6

Since the number of boys in Team Y is more than 90, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of students
= 60 u + 70 u
= 130 u
= 130 x 5
= 650

Answer(s): (a) 17 : 9; (b) 650