PSLE The number of girls and boys taking part in a contest are in the ratio 1 : 2. These students are put into two teams. 40% of the girls and 30% of the boys are in Team Y. The rest of the students are in Team Z.
- What is the ratio of the number of students in Team Z to Team Y? Give your answer in the simplest form.
- The number of boys in Team Y is more than 80. What is the smallest possible total number of students taking part in the contest?
Girls |
Boys |
10 u |
20 u |
Team Y |
Team Z |
Team Y |
Team Z |
4 u |
6 u |
6 u |
14 u |
(a)
Girls : Boys
1 : 2
10 : 20
Number of girls in Team Y
= 40% x 10 u
=
40100 x 10 u
= 4 u
Number of girls in Team Z
= 10 u - 4 u
= 6 u
Number of boys in Team Y
= 30% x 20 u
=
30100 x 20 u
= 6 u
Number of boys in Team Z
= 20 u - 6 u
= 14 u
Team Y : Team Z
6 + 14 : 4 + 6
20 : 10
(÷10)2 : 1
(b)
Number of boys in Team Y = 6 u
Since the number of boys in Team Y is 6 u, it must be multiple of 6.
Number of sets of 6
= 80 ÷ 6
= 13 r 2
Since the number of boys in Team Y is more than 80, the number of sets must be 1 more than 13.
1 u = 13 + 1 = 14
Smallest possible number of students
= 10 u + 20 u
= 30 u
= 30 x 14
= 420
Answer(s): (a) 2 : 1; (b) 420