PSLE The number of boys and girls taking part in a test are in the ratio 1 : 7. These students are put into two teams. 60% of the boys and 20% of the girls are in Team E. The rest of the students are in Team F.
- What is the ratio of the number of students in Team F to Team E? Give your answer in the simplest form.
- The number of girls in Team E is more than 80. What is the smallest possible total number of students taking part in the test?
Boys |
Girls |
10 u |
70 u |
Team E |
Team F |
Team E |
Team F |
6 u |
4 u |
14 u |
56 u |
(a)
Boys : Girls
1 : 7
10 : 70
Number of boys in Team E
= 60% x 10 u
=
60100 x 10 u
= 6 u
Number of boys in Team F
= 10 u - 6 u
= 4 u
Number of girls in Team E
= 20% x 70 u
=
20100 x 70 u
= 14 u
Number of girls in Team F
= 70 u - 14 u
= 56 u
Team E : Team F
4 + 56 : 6 + 14
60 : 20
(÷20)3 : 1
(b)
Number of girls in Team E = 14 u
Since the number of girls in Team E is 14 u, it must be multiple of 14.
Number of sets of 14
= 80 ÷ 14
= 5 r 10
Since the number of girls in Team E is more than 80, the number of sets must be 1 more than 5.
1 u = 5 + 1 = 6
Smallest possible number of students
= 10 u + 70 u
= 80 u
= 80 x 6
= 480
Answer(s): (a) 3 : 1; (b) 480