The ratio of the boys to the girls in a school was 5 : 3. After 29 boys went home and 18 new girls came, there were 19 more boys than girls in the end. Find the number of students in the school at first.
| |
Boys
(1) |
Girls
(2) |
(3) |
| Before |
5 u |
3 u |
3 u |
| Change |
- 29 |
+ 18 |
+ 18 + 19 = + 37 |
| After |
5 u |
3 u + 18 |
3 u + 37 |
Comparing boys and
girls in the end |
19 more |
|
|
Since the number of boys is 19 more than the number of girls in the end, when we
add 19 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
5 u - 29 = 3 u + 37
5 u - 3 u = 37 + 29
2 u = 66
1 u = 66 ÷ 2 = 33
Number of students at first
= 5 u + 3 u
= 8 u
= 8 x 33
= 264
Answer(s): 264
