In a school, the ratio of children to the number of adults is 8 : 1.
The ratio of the number of men to the number of women is 8 : 5.
There are 90 more men than women.
How many people are there in the school?
| Children |
Adults |
| 8 x 13 |
1 x 13 |
| |
Men |
Women |
| |
8 x 1 |
5 x 1 |
| 104 u |
8 u |
5 u |
The number of adults is the combined repeated identity.
Make the number of adults the same using the LCM of 1 and 13.
LCM of 1 and 13 = 13
Number of more men than women
= 8 u - 5 u
= 3 u
3 u = 90
1 u = 90 ÷ 3 = 30
Number of people
= 104 u + 8 u + 5 u
= 117 u
= 117 x 30
= 3510
Answer(s): 3510
