PSLE The number of girls and boys taking part in a quiz are in the ratio 5 : 4. These students are put into two teams. 70% of the girls and 10% of the boys are in Team F. The rest of the students are in Team G.
- What is the ratio of the number of students in Team G to Team F? Give your answer in the simplest form.
- The number of boys in Team F is more than 30. What is the smallest possible total number of students taking part in the quiz?
Girls |
Boys |
50 u |
40 u |
Team F |
Team G |
Team F |
Team G |
35 u |
15 u |
4 u |
36 u |
(a)
Girls : Boys
5 : 4
50 : 40
Number of girls in Team F
= 70% x 50 u
=
70100 x 50 u
= 35 u
Number of girls in Team G
= 50 u - 35 u
= 15 u
Number of boys in Team F
= 10% x 40 u
=
10100 x 40 u
= 4 u
Number of boys in Team G
= 40 u - 4 u
= 36 u
Team F : Team G
15 + 36 : 35 + 4
51 : 39
(÷3)17 : 13
(b)
Number of boys in Team F = 4 u
Since the number of boys in Team F is 4 u, it must be multiple of 4.
Number of sets of 4
= 30 ÷ 4
= 7 r 2
Since the number of boys in Team F is more than 30, the number of sets must be 1 more than 7.
1 u = 7 + 1 = 8
Smallest possible number of students
= 50 u + 40 u
= 90 u
= 90 x 8
= 720
Answer(s): (a) 17 : 13; (b) 720