PSLE The number of boys and girls taking part in a quiz are in the ratio 8 : 7. These students are put into two teams. 70% of the boys and 10% of the girls are in Team V. The rest of the students are in Team W.
- What is the ratio of the number of students in Team W to Team V? Give your answer in the simplest form.
- The number of girls in Team V is more than 30. What is the smallest possible total number of students taking part in the quiz?
Boys |
Girls |
80 u |
70 u |
Team V |
Team W |
Team V |
Team W |
56 u |
24 u |
7 u |
63 u |
(a)
Boys : Girls
8 : 7
80 : 70
Number of boys in Team V
= 70% x 80 u
=
70100 x 80 u
= 56 u
Number of boys in Team W
= 80 u - 56 u
= 24 u
Number of girls in Team V
= 10% x 70 u
=
10100 x 70 u
= 7 u
Number of girls in Team W
= 70 u - 7 u
= 63 u
Team V : Team W
24 + 63 : 56 + 7
87 : 63
(÷3)29 : 21
(b)
Number of girls in Team V = 7 u
Since the number of girls in Team V is 7 u, it must be multiple of 7.
Number of sets of 7
= 30 ÷ 7
= 4 r 2
Since the number of girls in Team V is more than 30, the number of sets must be 1 more than 4.
1 u = 4 + 1 = 5
Smallest possible number of students
= 80 u + 70 u
= 150 u
= 150 x 5
= 750
Answer(s): (a) 29 : 21; (b) 750