The ratio of the girls to the boys in a school was 8 : 3. After 14 girls went home and 11 new boys came, there were 10 more girls than boys in the end. Find the number of pupils in the school at first.
| |
Girls
(1) |
Boys
(2) |
(3) |
| Before |
8 u |
3 u |
3 u |
| Change |
- 14 |
+ 11 |
+ 11 + 10 = + 21 |
| After |
8 u |
3 u + 11 |
3 u + 21 |
Comparing girls and
boys in the end |
10 more |
|
|
Since the number of girls is 10 more than the number of boys in the end, when we
add 10 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
8 u - 14 = 3 u + 21
8 u - 3 u = 21 + 14
5 u = 35
1 u = 35 ÷ 5 = 7
Number of pupils at first
= 8 u + 3 u
= 11 u
= 11 x 7
= 77
Answer(s): 77
