The ratio of the boys to the girls in a school was 7 : 4. After 13 boys went home and 17 new girls came, there were 12 more boys than girls in the end. Find the number of children in the school in the end.
|
Boys (1) |
Girls (2) |
(3) |
Before |
7 u |
4 u |
4 u |
Change |
- 13 |
+ 17 |
+ 17 + 12 = + 29 |
After |
7 u |
4 u + 17 |
4 u + 29 |
Comparing boys and girls in the end |
12 more |
|
|
Since the number of boys is 12 more than the number of girls in the end, when we
add 12 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
7 u - 13 = 4 u + 29
7 u - 4 u = 29 + 13
3 u = 42
1 u = 42 ÷ 3 = 14
Number of children in the end
= 7 u + 4 u - 13 + 17
= 11 u + 4
= 11 x 14 + 4
= 154 + 4
= 158
Answer(s): 158