In a school, the ratio of children to the number of adults is 5 : 2.
The ratio of the number of women to the number of men is 5 : 4.
There are 42 less men than women.
How many people are there in the school?
| Children |
Adults |
| 5 x 9 |
2 x 9 |
| |
Women |
Men |
| |
5 x 2 |
4 x 2 |
| 45 u |
10 u |
8 u |
The number of adults is the combined repeated identity.
Make the number of adults the same using the LCM of 2 and 9.
LCM of 2 and 9 = 18
Number of less men than women
= 10 u - 8 u
= 2 u
2 u = 42
1 u = 42 ÷ 2 = 21
Number of people
= 45 u + 10 u + 8 u
= 63 u
= 63 x 21
= 1323
Answer(s): 1323
