PSLE The number of girls and boys taking part in a quiz are in the ratio 3 : 8. These students are put into two teams. 20% of the girls and 60% of the boys are in Team A. The rest of the students are in Team B.
- What is the ratio of the number of students in Team B to Team A? Give your answer in the simplest form.
- The number of girls in Team B is fewer than 70. What is the largest possible total number of students taking part in the quiz?
Girls |
Boys |
30 u |
80 u |
Team A |
Team B |
Team A |
Team B |
6 u |
24 u |
48 u |
32 u |
(a)
Girls : Boys
3 : 8
30 : 80
Number of girls in Team A
= 20% x 30 u
=
20100 x 30 u
= 6 u
Number of girls in Team B
= 30 u - 6 u
= 24 u
Number of boys in Team A
= 60% x 80 u
=
60100 x 80 u
= 48 u
Number of boys in Team B
= 80 u - 48 u
= 32 u
Team B : Team A
24 + 32 : 6 + 48
56 : 54
(÷2)28 : 27
(b)
Number of girls in Team B = 24 u
Since the number of girls in Team B is 24 u, it must be multiple of 24.
Number of sets of 24
= 70 ÷ 24
= 2 r 22
Since the number of girls in Team B is less than 70, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 30 u + 80 u
= 110 u
= 110 x 2
= 220
Answer(s): (a) 28 : 27; (b) 220