The ratio of the boys to the girls in a school was 7 : 3. After 19 boys went home and 12 new girls came, there were 17 more boys than girls in the end. Find the number of children in the school at first.
| |
Boys
(1) |
Girls
(2) |
(3) |
| Before |
7 u |
3 u |
3 u |
| Change |
- 19 |
+ 12 |
+ 12 + 17 = + 29 |
| After |
7 u |
3 u + 12 |
3 u + 29 |
Comparing boys and
girls in the end |
17 more |
|
|
Since the number of boys is 17 more than the number of girls in the end, when we
add 17 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
7 u - 19 = 3 u + 29
7 u - 3 u = 29 + 19
4 u = 48
1 u = 48 ÷ 4 = 12
Number of children at first
= 7 u + 3 u
= 10 u
= 10 x 12
= 120
Answer(s): 120
