The ratio of the girls to the boys in a school was 5 : 3. After 10 girls went home and 25 new boys came, there were 9 more girls than boys in the end. Find the number of students in the school at first.
|
Girls (1) |
Boys (2) |
(3) |
Before |
5 u |
3 u |
3 u |
Change |
- 10 |
+ 25 |
+ 25 + 9 = + 34 |
After |
5 u |
3 u + 25 |
3 u + 34 |
Comparing girls and boys in the end |
9 more |
|
|
Since the number of girls is 9 more than the number of boys in the end, when we
add 9 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
5 u - 10 = 3 u + 34
5 u - 3 u = 34 + 10
2 u = 44
1 u = 44 ÷ 2 = 22
Number of students at first
= 5 u + 3 u
= 8 u
= 8 x 22
= 176
Answer(s): 176