PSLE The number of girls and boys taking part in a contest are in the ratio 3 : 7. These students are put into two teams. 30% of the girls and 50% of the boys 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 boys in Team N is more than 80. What is the smallest possible total number of students taking part in the contest?
Girls |
Boys |
30 u |
70 u |
Team N |
Team P |
Team N |
Team P |
9 u |
21 u |
35 u |
35 u |
(a)
Girls : Boys
3 : 7
30 : 70
Number of girls in Team N
= 30% x 30 u
=
30100 x 30 u
= 9 u
Number of girls in Team P
= 30 u - 9 u
= 21 u
Number of boys in Team N
= 50% x 70 u
=
50100 x 70 u
= 35 u
Number of boys in Team P
= 70 u - 35 u
= 35 u
Team N : Team P
21 + 35 : 9 + 35
56 : 44
(÷4)14 : 11
(b)
Number of boys in Team N = 35 u
Since the number of boys in Team N is 35 u, it must be multiple of 35.
Number of sets of 35
= 80 ÷ 35
= 2 r 10
Since the number of boys in Team N is more than 80, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 30 u + 70 u
= 100 u
= 100 x 3
= 300
Answer(s): (a) 14 : 11; (b) 300