In a school, the ratio of adults to the number of children is 4 : 9.
The ratio of the number of boys to the number of girls is 8 : 5.
There are 54 more boys than girls.
How many people are there in the school?
Adults |
Children |
4 x 13 |
9 x 13 |
|
Boys |
Girls |
|
8 x 9 |
5 x 9 |
52 u |
72 u |
45 u |
The number of children is the combined repeated identity.
Make the number of children the same using the LCM of 9 and 13.
LCM of 9 and 13 = 117
Number of more boys than girls
= 72 u - 45 u
= 27 u
27 u = 54
1 u = 54 ÷ 27 = 2
Number of people
= 52 u + 72 u + 45 u
= 169 u
= 169 x 2
= 338
Answer(s): 338