PSLE The number of girls and boys taking part in a contest are in the ratio 1 : 4. These students are put into two teams. 60% of the girls and 40% 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 boys in Team A is more than 40. What is the smallest possible total number of students taking part in the contest?
Girls |
Boys |
10 u |
40 u |
Team A |
Team B |
Team A |
Team B |
6 u |
4 u |
16 u |
24 u |
(a)
Girls : Boys
1 : 4
10 : 40
Number of girls in Team A
= 60% x 10 u
=
60100 x 10 u
= 6 u
Number of girls in Team B
= 10 u - 6 u
= 4 u
Number of boys in Team A
= 40% x 40 u
=
40100 x 40 u
= 16 u
Number of boys in Team B
= 40 u - 16 u
= 24 u
Team A : Team B
4 + 24 : 6 + 16
28 : 22
(÷2)14 : 11
(b)
Number of boys in Team A = 16 u
Since the number of boys in Team A is 16 u, it must be multiple of 16.
Number of sets of 16
= 40 ÷ 16
= 2 r 8
Since the number of boys in Team A is more than 40, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 10 u + 40 u
= 50 u
= 50 x 3
= 150
Answer(s): (a) 14 : 11; (b) 150