The ratio of the boys to the girls in a school was 5 : 3. After 25 boys went home and 30 new girls came, there were 13 more boys than girls in the end. Find the number of children in the school in the end.
| |
Boys
(1) |
Girls
(2) |
(3) |
| Before |
5 u |
3 u |
3 u |
| Change |
- 25 |
+ 30 |
+ 30 + 13 = + 43 |
| After |
5 u |
3 u + 30 |
3 u + 43 |
Comparing boys and
girls in the end |
13 more |
|
|
Since the number of boys is 13 more than the number of girls in the end, when we
add 13 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
5 u - 25 = 3 u + 43
5 u - 3 u = 43 + 25
2 u = 68
1 u = 68 ÷ 2 = 34
Number of children in the end
= 5 u + 3 u - 25 + 30
= 8 u + 5
= 8 x 34 + 5
= 272 + 5
= 277
Answer(s): 277
