PSLE The number of boys and girls taking part in a quiz are in the ratio 7 : 2. These students are put into two teams. 40% of the boys and 20% of the girls are in Team P. The rest of the students are in Team Q.
- What is the ratio of the number of students in Team Q to Team P? Give your answer in the simplest form.
- The number of girls in Team P is more than 90. What is the smallest possible total number of students taking part in the quiz?
Boys |
Girls |
70 u |
20 u |
Team P |
Team Q |
Team P |
Team Q |
28 u |
42 u |
4 u |
16 u |
(a)
Boys : Girls
7 : 2
70 : 20
Number of boys in Team P
= 40% x 70 u
=
40100 x 70 u
= 28 u
Number of boys in Team Q
= 70 u - 28 u
= 42 u
Number of girls in Team P
= 20% x 20 u
=
20100 x 20 u
= 4 u
Number of girls in Team Q
= 20 u - 4 u
= 16 u
Team P : Team Q
42 + 16 : 28 + 4
58 : 32
(÷2)29 : 16
(b)
Number of girls in Team P = 4 u
Since the number of girls in Team P is 4 u, it must be multiple of 4.
Number of sets of 4
= 90 ÷ 4
= 22 r 2
Since the number of girls in Team P is more than 90, the number of sets must be 1 more than 22.
1 u = 22 + 1 = 23
Smallest possible number of students
= 70 u + 20 u
= 90 u
= 90 x 23
= 2070
Answer(s): (a) 29 : 16; (b) 2070