The ratio of the boys to the girls in a school was 5 : 3. After 17 boys went home and 12 new girls came, there were 13 more boys than girls in the end. Find the number of pupils in the school at first.
| |
Boys
(1) |
Girls
(2) |
(3) |
| Before |
5 u |
3 u |
3 u |
| Change |
- 17 |
+ 12 |
+ 12 + 13 = + 25 |
| After |
5 u |
3 u + 12 |
3 u + 25 |
Comparing boys and
girls in the end |
13 more |
|
|
Since the number of boys is 13 more than the number of girls in the end, when we
add 13 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
5 u - 17 = 3 u + 25
5 u - 3 u = 25 + 17
2 u = 42
1 u = 42 ÷ 2 = 21
Number of pupils at first
= 5 u + 3 u
= 8 u
= 8 x 21
= 168
Answer(s): 168
