PSLE The number of boys and girls taking part in a contest are in the ratio 7 : 8. These students are put into two teams. 80% of the boys and 20% of the girls are in Team U. The rest of the students are in Team V.
- What is the ratio of the number of students in Team V to Team U? Give your answer in the simplest form.
- The number of boys in Team V is fewer than 40. What is the largest possible total number of students taking part in the contest?
Boys |
Girls |
70 u |
80 u |
Team U |
Team V |
Team U |
Team V |
56 u |
14 u |
16 u |
64 u |
(a)
Boys : Girls
7 : 8
70 : 80
Number of boys in Team U
= 80% x 70 u
=
80100 x 70 u
= 56 u
Number of boys in Team V
= 70 u - 56 u
= 14 u
Number of girls in Team U
= 20% x 80 u
=
20100 x 80 u
= 16 u
Number of girls in Team V
= 80 u - 16 u
= 64 u
Team V : Team U
14 + 64 : 56 + 16
78 : 72
(÷6)13 : 12
(b)
Number of boys in Team V = 14 u
Since the number of boys in Team V is 14 u, it must be multiple of 14.
Number of sets of 14
= 40 ÷ 14
= 2 r 12
Since the number of boys in Team V is less than 40, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 70 u + 80 u
= 150 u
= 150 x 2
= 300
Answer(s): (a) 13 : 12; (b) 300