PSLE The number of girls and boys taking part in a contest are in the ratio 3 : 4. These pupils are put into two teams. 40% of the girls and 20% of the boys are in Team Y. The rest of the pupils are in Team Z.
- What is the ratio of the number of pupils in Team Z to Team Y? Give your answer in the simplest form.
- The number of girls in Team Z is fewer than 70. What is the largest possible total number of pupils taking part in the contest?
Girls |
Boys |
30 u |
40 u |
Team Y |
Team Z |
Team Y |
Team Z |
12 u |
18 u |
8 u |
32 u |
(a)
Girls : Boys
3 : 4
30 : 40
Number of girls in Team Y
= 40% x 30 u
=
40100 x 30 u
= 12 u
Number of girls in Team Z
= 30 u - 12 u
= 18 u
Number of boys in Team Y
= 20% x 40 u
=
20100 x 40 u
= 8 u
Number of boys in Team Z
= 40 u - 8 u
= 32 u
Team Z : Team Y
18 + 32 : 12 + 8
50 : 20
(÷10)5 : 2
(b)
Number of girls in Team Z = 18 u
Since the number of girls in Team Z is 18 u, it must be multiple of 18.
Number of sets of 18
= 70 ÷ 18
= 3 r 16
Since the number of girls in Team Z is less than 70, the number of sets must be 3.
1 u = 3
Largest possible number of pupils
= 30 u + 40 u
= 70 u
= 70 x 3
= 210
Answer(s): (a) 5 : 2; (b) 210