The ratio of the boys to the girls in a school was 8 : 5. After 12 boys went home and 13 new girls came, there were 8 more boys than girls in the end. Find the number of children in the school at first.
| |
Boys
(1) |
Girls
(2) |
(3) |
| Before |
8 u |
5 u |
5 u |
| Change |
- 12 |
+ 13 |
+ 13 + 8 = + 21 |
| After |
8 u |
5 u + 13 |
5 u + 21 |
Comparing boys and
girls in the end |
8 more |
|
|
Since the number of boys is 8 more than the number of girls in the end, when we
add 8 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
8 u - 12 = 5 u + 21
8 u - 5 u = 21 + 12
3 u = 33
1 u = 33 ÷ 3 = 11
Number of children at first
= 8 u + 5 u
= 13 u
= 13 x 11
= 143
Answer(s): 143
