The ratio of the boys to the girls in a school was 7 : 2. After 11 boys went home and 12 new girls came, there were 7 more boys than girls in the end. Find the number of pupils in the school at first.
|
Boys (1) |
Girls (2) |
(3) |
Before |
7 u |
2 u |
2 u |
Change |
- 11 |
+ 12 |
+ 12 + 7 = + 19 |
After |
7 u |
2 u + 12 |
2 u + 19 |
Comparing boys and girls in the end |
7 more |
|
|
Since the number of boys is 7 more than the number of girls in the end, when we
add 7 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
7 u - 11 = 2 u + 19
7 u - 2 u = 19 + 11
5 u = 30
1 u = 30 ÷ 5 = 6
Number of pupils at first
= 7 u + 2 u
= 9 u
= 9 x 6
= 54
Answer(s): 54