At a school sports festival,
16 of the participants were P5 and P6 students.
35 of the remaining participants were P3 and P4 students. The rest were P1 and P2 students in the ratio of 2 : 5 respectively. There were 42 fewer P1 students than the total number of P5 and P6 students. How many students were there at the school sports festival?
P1 |
P2 |
P3 |
P4 |
P5 |
P6 |
Total |
5x7 |
1x7 |
6x7 |
2x7 |
3x7 |
|
|
2x2 |
5x2 |
|
|
|
|
|
4 u |
10 u |
21 u |
7 u |
42 u |
The total number of P1 and P2 students is the combined repeated identity. Make the total number of P1 and P2 students the same. LCM of 2 and 7 is 14.
The total number of P1, P2, P3 and P4 students is another combined repeated identity. Make the total number of P1, P2, P3 and P4 students the same. LCM of 35 and 5 is 35.
Number of fewer P1 students than the total number of P5 and P6 students
= 7 u - 4 u
= 3 u
3 u = 42
1 u = 42 ÷ 3 = 14
Total number of students at the sports festival
= 42 u
= 42 x 14
= 588
Answer(s): 588