PSLE The number of boys and girls taking part in a test are in the ratio 6 : 7. These students are put into two teams. 60% of the boys and 20% of the girls 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 U is fewer than 70. What is the largest possible total number of students taking part in the test?
Boys |
Girls |
60 u |
70 u |
Team T |
Team U |
Team T |
Team U |
36 u |
24 u |
14 u |
56 u |
(a)
Boys : Girls
6 : 7
60 : 70
Number of boys in Team T
= 60% x 60 u
=
60100 x 60 u
= 36 u
Number of boys in Team U
= 60 u - 36 u
= 24 u
Number of girls in Team T
= 20% x 70 u
=
20100 x 70 u
= 14 u
Number of girls in Team U
= 70 u - 14 u
= 56 u
Team U : Team T
24 + 56 : 36 + 14
80 : 50
(÷10)8 : 5
(b)
Number of boys in Team U = 24 u
Since the number of boys in Team U is 24 u, it must be multiple of 24.
Number of sets of 24
= 70 ÷ 24
= 2 r 22
Since the number of boys in Team U is less than 70, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 60 u + 70 u
= 130 u
= 130 x 2
= 260
Answer(s): (a) 8 : 5; (b) 260