PSLE The number of boys and girls taking part in a contest are in the ratio 2 : 7. These students are put into two teams. 70% of the boys and 30% 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 60. What is the smallest possible total number of students taking part in the contest?
Boys |
Girls |
20 u |
70 u |
Team E |
Team F |
Team E |
Team F |
14 u |
6 u |
21 u |
49 u |
(a)
Boys : Girls
2 : 7
20 : 70
Number of boys in Team E
= 70% x 20 u
=
70100 x 20 u
= 14 u
Number of boys in Team F
= 20 u - 14 u
= 6 u
Number of girls in Team E
= 30% x 70 u
=
30100 x 70 u
= 21 u
Number of girls in Team F
= 70 u - 21 u
= 49 u
Team E : Team F
6 + 49 : 14 + 21
55 : 35
(÷5)11 : 7
(b)
Number of girls in Team E = 21 u
Since the number of girls in Team E is 21 u, it must be multiple of 21.
Number of sets of 21
= 60 ÷ 21
= 2 r 18
Since the number of girls in Team E is more than 60, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 20 u + 70 u
= 90 u
= 90 x 3
= 270
Answer(s): (a) 11 : 7; (b) 270