The ratio of the girls to the boys in a school was 7 : 3. After 10 girls went home and 30 new boys came, there were 12 more girls than boys in the end. Find the number of pupils in the school in the end.
| |
Girls
(1) |
Boys
(2) |
(3) |
| Before |
7 u |
3 u |
3 u |
| Change |
- 10 |
+ 30 |
+ 30 + 12 = + 42 |
| After |
7 u |
3 u + 30 |
3 u + 42 |
Comparing girls and
boys in the end |
12 more |
|
|
Since the number of girls is 12 more than the number of boys in the end, when we
add 12 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
7 u - 10 = 3 u + 42
7 u - 3 u = 42 + 10
4 u = 52
1 u = 52 ÷ 4 = 13
Number of pupils in the end
= 7 u + 3 u - 10 + 30
= 10 u + 20
= 10 x 13 + 20
= 130 + 20
= 150
Answer(s): 150
