The ratio of the girls to the boys in a school was 5 : 3. After 13 girls went home and 10 new boys came, there were 15 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 |
- 13 |
+ 10 |
+ 10 + 15 = + 25 |
| After |
5 u |
3 u + 10 |
3 u + 25 |
Comparing girls and
boys in the end |
15 more |
|
|
Since the number of girls is 15 more than the number of boys in the end, when we
add 15 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
5 u - 13 = 3 u + 25
5 u - 3 u = 25 + 13
2 u = 38
1 u = 38 ÷ 2 = 19
Number of students at first
= 5 u + 3 u
= 8 u
= 8 x 19
= 152
Answer(s): 152
