In a school, the ratio of children to the number of adults is 4 : 1.
The ratio of the number of men to the number of women is 3 : 1.
There are 82 more men than women.
How many people are there in the school?
Children |
Adults |
4 x 4 |
1 x 4 |
|
Men |
Women |
|
3 x 1 |
1 x 1 |
16 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 men than women
= 3 u - 1 u
= 2 u
2 u = 82
1 u = 82 ÷ 2 = 41
Number of people
= 16 u + 3 u + 1 u
= 20 u
= 20 x 41
= 820
Answer(s): 820