The ratio of the boys to the girls in a school was 8 : 5. After 14 boys went home and 21 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 |
8 u |
5 u |
5 u |
Change |
- 14 |
+ 21 |
+ 21 + 7 = + 28 |
After |
8 u |
5 u + 21 |
5 u + 28 |
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)
8 u - 14 = 5 u + 28
8 u - 5 u = 28 + 14
3 u = 42
1 u = 42 ÷ 3 = 14
Number of pupils at first
= 8 u + 5 u
= 13 u
= 13 x 14
= 182
Answer(s): 182