PSLE The number of boys and girls taking part in a quiz are in the ratio 5 : 3. These students are put into two teams. 30% of the boys and 50% 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 80. What is the smallest possible total number of students taking part in the quiz?
Boys |
Girls |
50 u |
30 u |
Team N |
Team P |
Team N |
Team P |
15 u |
35 u |
15 u |
15 u |
(a)
Boys : Girls
5 : 3
50 : 30
Number of boys in Team N
= 30% x 50 u
=
30100 x 50 u
= 15 u
Number of boys in Team P
= 50 u - 15 u
= 35 u
Number of girls in Team N
= 50% x 30 u
=
50100 x 30 u
= 15 u
Number of girls in Team P
= 30 u - 15 u
= 15 u
Team N : Team P
35 + 15 : 15 + 15
50 : 30
(÷10)5 : 3
(b)
Number of girls in Team N = 15 u
Since the number of girls in Team N is 15 u, it must be multiple of 15.
Number of sets of 15
= 80 ÷ 15
= 5 r 5
Since the number of girls in Team N is more than 80, the number of sets must be 1 more than 5.
1 u = 5 + 1 = 6
Smallest possible number of students
= 50 u + 30 u
= 80 u
= 80 x 6
= 480
Answer(s): (a) 5 : 3; (b) 480