The ratio of the girls to the boys in a school was 5 : 2. After 14 girls went home and 17 new boys came, there were 14 more girls than boys in the end. Find the number of students in the school in the end.
| |
Girls
(1) |
Boys
(2) |
(3) |
| Before |
5 u |
2 u |
2 u |
| Change |
- 14 |
+ 17 |
+ 17 + 14 = + 31 |
| After |
5 u |
2 u + 17 |
2 u + 31 |
Comparing girls and
boys in the end |
14 more |
|
|
Since the number of girls is 14 more than the number of boys in the end, when we
add 14 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
5 u - 14 = 2 u + 31
5 u - 2 u = 31 + 14
3 u = 45
1 u = 45 ÷ 3 = 15
Number of students in the end
= 5 u + 2 u - 14 + 17
= 7 u + 3
= 7 x 15 + 3
= 105 + 3
= 108
Answer(s): 108
