PSLE The number of boys and girls taking part in a quiz are in the ratio 2 : 5. These students are put into two teams. 30% of the boys and 40% of the girls are in Team X. The rest of the students are in Team Y.
- What is the ratio of the number of students in Team Y to Team X? Give your answer in the simplest form.
- The number of boys in Team Y is fewer than 60. What is the largest possible total number of students taking part in the quiz?
Boys |
Girls |
20 u |
50 u |
Team X |
Team Y |
Team X |
Team Y |
6 u |
14 u |
20 u |
30 u |
(a)
Boys : Girls
2 : 5
20 : 50
Number of boys in Team X
= 30% x 20 u
=
30100 x 20 u
= 6 u
Number of boys in Team Y
= 20 u - 6 u
= 14 u
Number of girls in Team X
= 40% x 50 u
=
40100 x 50 u
= 20 u
Number of girls in Team Y
= 50 u - 20 u
= 30 u
Team Y : Team X
14 + 30 : 6 + 20
44 : 26
(÷2)22 : 13
(b)
Number of boys in Team Y = 14 u
Since the number of boys in Team Y is 14 u, it must be multiple of 14.
Number of sets of 14
= 60 ÷ 14
= 4 r 4
Since the number of boys in Team Y is less than 60, the number of sets must be 4.
1 u = 4
Largest possible number of students
= 20 u + 50 u
= 70 u
= 70 x 4
= 280
Answer(s): (a) 22 : 13; (b) 280