PSLE The contestants at a contest are divided in Group A and Group B. The ratio of the number of boys to girls in Group A is 7 : 3. The ratio of the number of boys to girls in Group B is 5 : 1. There are 3 times as many contestants in Group B as in Group A. There are 126 more boys in Group B than Group A. What is the total number of contestants?
Group A |
Group B |
10 u |
6x5 = 30 u |
Boys |
Girls |
Boys |
Girls |
7 u |
3 u |
5x5 = 25 u |
1x5 = 5 u
|
Total number of contestants in Group A
= 7 u + 3 u
= 10 u
Total number of contestants in Group B
= 3 x 10 u
= 30 u
The total number of contestants in Group B is repeated.
Use LCM to make the total number of contestants in Group B the same.
LCM of 30 and 6 is 30.
Number of more boys in Group B than Group A
= 25 u - 7 u
= 18 u
18 u = 126
1 u = 126 ÷ 18 = 7
Total number of contestants
= 7 u + 3 u + 25 u + 5 u
= 40 u
= 40 x 7
= 280
Answer(s): 280