PSLE The number of boys and girls taking part in a quiz are in the ratio 4 : 3. These students are put into two teams. 30% of the boys and 20% of the girls are in Team N. The rest of the students are in Team P.
- What is the ratio of the number of students in Team P to Team N? Give your answer in the simplest form.
- The number of girls in Team N is more than 70. What is the smallest possible total number of students taking part in the quiz?
Boys |
Girls |
40 u |
30 u |
Team N |
Team P |
Team N |
Team P |
12 u |
28 u |
6 u |
24 u |
(a)
Boys : Girls
4 : 3
40 : 30
Number of boys in Team N
= 30% x 40 u
=
30100 x 40 u
= 12 u
Number of boys in Team P
= 40 u - 12 u
= 28 u
Number of girls in Team N
= 20% x 30 u
=
20100 x 30 u
= 6 u
Number of girls in Team P
= 30 u - 6 u
= 24 u
Team N : Team P
28 + 24 : 12 + 6
52 : 18
(÷2)26 : 9
(b)
Number of girls in Team N = 6 u
Since the number of girls in Team N is 6 u, it must be multiple of 6.
Number of sets of 6
= 70 ÷ 6
= 11 r 4
Since the number of girls in Team N is more than 70, the number of sets must be 1 more than 11.
1 u = 11 + 1 = 12
Smallest possible number of students
= 40 u + 30 u
= 70 u
= 70 x 12
= 840
Answer(s): (a) 26 : 9; (b) 840