PSLE The number of boys and girls taking part in a test are in the ratio 3 : 4. These pupils are put into two teams. 30% of the boys and 40% of the girls are in Team F. The rest of the pupils are in Team G.
- What is the ratio of the number of pupils in Team G to Team F? Give your answer in the simplest form.
- The number of girls in Team F is more than 70. What is the smallest possible total number of pupils taking part in the test?
Boys |
Girls |
30 u |
40 u |
Team F |
Team G |
Team F |
Team G |
9 u |
21 u |
16 u |
24 u |
(a)
Boys : Girls
3 : 4
30 : 40
Number of boys in Team F
= 30% x 30 u
=
30100 x 30 u
= 9 u
Number of boys in Team G
= 30 u - 9 u
= 21 u
Number of girls in Team F
= 40% x 40 u
=
40100 x 40 u
= 16 u
Number of girls in Team G
= 40 u - 16 u
= 24 u
Team F : Team G
21 + 24 : 9 + 16
45 : 25
(÷5)9 : 5
(b)
Number of girls in Team F = 16 u
Since the number of girls in Team F is 16 u, it must be multiple of 16.
Number of sets of 16
= 70 ÷ 16
= 4 r 6
Since the number of girls in Team F is more than 70, the number of sets must be 1 more than 4.
1 u = 4 + 1 = 5
Smallest possible number of pupils
= 30 u + 40 u
= 70 u
= 70 x 5
= 350
Answer(s): (a) 9 : 5; (b) 350