PSLE The number of girls and boys taking part in a quiz are in the ratio 3 : 7. These pupils are put into two teams. 70% of the girls and 10% of the boys are in Team S. The rest of the pupils are in Team T.
- What is the ratio of the number of pupils in Team T to Team S? Give your answer in the simplest form.
- The number of boys in Team S is more than 30. What is the smallest possible total number of pupils taking part in the quiz?
Girls |
Boys |
30 u |
70 u |
Team S |
Team T |
Team S |
Team T |
21 u |
9 u |
7 u |
63 u |
(a)
Girls : Boys
3 : 7
30 : 70
Number of girls in Team S
= 70% x 30 u
=
70100 x 30 u
= 21 u
Number of girls in Team T
= 30 u - 21 u
= 9 u
Number of boys in Team S
= 10% x 70 u
=
10100 x 70 u
= 7 u
Number of boys in Team T
= 70 u - 7 u
= 63 u
Team S : Team T
9 + 63 : 21 + 7
72 : 28
(÷4)18 : 7
(b)
Number of boys in Team S = 7 u
Since the number of boys in Team S is 7 u, it must be multiple of 7.
Number of sets of 7
= 30 ÷ 7
= 4 r 2
Since the number of boys in Team S is more than 30, the number of sets must be 1 more than 4.
1 u = 4 + 1 = 5
Smallest possible number of pupils
= 30 u + 70 u
= 100 u
= 100 x 5
= 500
Answer(s): (a) 18 : 7; (b) 500