PSLE The number of girls and boys taking part in a test are in the ratio 1 : 8. These students are put into two teams. 70% of the girls and 10% of the boys are in Team T. The rest of the students are in Team U.
- What is the ratio of the number of students in Team U to Team T? Give your answer in the simplest form.
- The number of boys in Team T is more than 90. What is the smallest possible total number of students taking part in the test?
Girls |
Boys |
10 u |
80 u |
Team T |
Team U |
Team T |
Team U |
7 u |
3 u |
8 u |
72 u |
(a)
Girls : Boys
1 : 8
10 : 80
Number of girls in Team T
= 70% x 10 u
=
70100 x 10 u
= 7 u
Number of girls in Team U
= 10 u - 7 u
= 3 u
Number of boys in Team T
= 10% x 80 u
=
10100 x 80 u
= 8 u
Number of boys in Team U
= 80 u - 8 u
= 72 u
Team T : Team U
3 + 72 : 7 + 8
75 : 15
(÷15)5 : 1
(b)
Number of boys in Team T = 8 u
Since the number of boys in Team T is 8 u, it must be multiple of 8.
Number of sets of 8
= 90 ÷ 8
= 11 r 2
Since the number of boys in Team T is more than 90, the number of sets must be 1 more than 11.
1 u = 11 + 1 = 12
Smallest possible number of students
= 10 u + 80 u
= 90 u
= 90 x 12
= 1080
Answer(s): (a) 5 : 1; (b) 1080