In a school, the ratio of adults to the number of children is 5 : 4.
The ratio of the number of boys to the number of girls is 8 : 5.
There are 84 more boys than girls.
How many people are there in the school?
| Adults |
Children |
| 5 x 13 |
4 x 13 |
| |
Boys |
Girls |
| |
8 x 4 |
5 x 4 |
| 65 u |
32 u |
20 u |
The number of children is the combined repeated identity.
Make the number of children the same using the LCM of 4 and 13.
LCM of 4 and 13 = 52
Number of more boys than girls
= 32 u - 20 u
= 12 u
12 u = 84
1 u = 84 ÷ 12 = 7
Number of people
= 65 u + 32 u + 20 u
= 117 u
= 117 x 7
= 819
Answer(s): 819
