In a school, the ratio of adults to the number of children is 2 : 1.
The ratio of the number of girls to the number of boys is 4 : 1.
There are 54 less boys than girls.
How many people are there in the school?
Adults |
Children |
2 x 5 |
1 x 5 |
|
Girls |
Boys |
|
4 x 1 |
1 x 1 |
10 u |
4 u |
1 u |
The number of children is the combined repeated identity.
Make the number of children the same using the LCM of 1 and 5.
LCM of 1 and 5 = 5
Number of less boys than girls
= 4 u - 1 u
= 3 u
3 u = 54
1 u = 54 ÷ 3 = 18
Number of people
= 10 u + 4 u + 1 u
= 15 u
= 15 x 18
= 270
Answer(s): 270