The ratio of the girls to the boys in a school was 7 : 4. After 28 girls went home and 22 new boys came, there were 19 more girls than boys in the end. Find the number of students in the school at first.
| |
Girls
(1) |
Boys
(2) |
(3) |
| Before |
7 u |
4 u |
4 u |
| Change |
- 28 |
+ 22 |
+ 22 + 19 = + 41 |
| After |
7 u |
4 u + 22 |
4 u + 41 |
Comparing girls and
boys in the end |
19 more |
|
|
Since the number of girls is 19 more than the number of boys in the end, when we
add 19 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
7 u - 28 = 4 u + 41
7 u - 4 u = 41 + 28
3 u = 69
1 u = 69 ÷ 3 = 23
Number of students at first
= 7 u + 4 u
= 11 u
= 11 x 23
= 253
Answer(s): 253
