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. 70% of the boys and 40% 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 boys in Team F is fewer than 50. What is the largest possible total number of students taking part in the test?
Boys |
Girls |
10 u |
70 u |
Team E |
Team F |
Team E |
Team F |
7 u |
3 u |
28 u |
42 u |
(a)
Boys : Girls
1 : 7
10 : 70
Number of boys in Team E
= 70% x 10 u
=
70100 x 10 u
= 7 u
Number of boys in Team F
= 10 u - 7 u
= 3 u
Number of girls in Team E
= 40% x 70 u
=
40100 x 70 u
= 28 u
Number of girls in Team F
= 70 u - 28 u
= 42 u
Team F : Team E
3 + 42 : 7 + 28
45 : 35
(÷5)9 : 7
(b)
Number of boys in Team F = 3 u
Since the number of boys in Team F is 3 u, it must be multiple of 3.
Number of sets of 3
= 50 ÷ 3
= 16 r 2
Since the number of boys in Team F is less than 50, the number of sets must be 16.
1 u = 16
Largest possible number of students
= 10 u + 70 u
= 80 u
= 80 x 16
= 1280
Answer(s): (a) 9 : 7; (b) 1280