The ratio of the girls to the boys in a school was 5 : 3. After 21 girls went home and 27 new boys came, there were 8 more girls than boys in the end. Find the number of children in the school in the end.
| |
Girls
(1) |
Boys
(2) |
(3) |
| Before |
5 u |
3 u |
3 u |
| Change |
- 21 |
+ 27 |
+ 27 + 8 = + 35 |
| After |
5 u |
3 u + 27 |
3 u + 35 |
Comparing girls and
boys in the end |
8 more |
|
|
Since the number of girls is 8 more than the number of boys in the end, when we
add 8 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
5 u - 21 = 3 u + 35
5 u - 3 u = 35 + 21
2 u = 56
1 u = 56 ÷ 2 = 28
Number of children in the end
= 5 u + 3 u - 21 + 27
= 8 u + 6
= 8 x 28 + 6
= 224 + 6
= 230
Answer(s): 230
