In a school, the ratio of children to the number of adults is 10 : 1.
The ratio of the number of women to the number of men is 3 : 1.
There are 76 more women than men.
How many people are there in the school?
| Children |
Adults |
| 10 x 4 |
1 x 4 |
| |
Women |
Men |
| |
3 x 1 |
1 x 1 |
| 40 u |
3 u |
1 u |
The number of adults is the combined repeated identity.
Make the number of adults the same using the LCM of 1 and 4.
LCM of 1 and 4 = 4
Number of more women than men
= 3 u - 1 u
= 2 u
2 u = 76
1 u = 76 ÷ 2 = 38
Number of people
= 40 u + 3 u + 1 u
= 44 u
= 44 x 38
= 1672
Answer(s): 1672
