The ratio of the girls to the boys in a school was 5 : 2. After 19 girls went home and 13 new boys came, there were 13 more girls than boys in the end. Find the number of pupils in the school at first.
| |
Girls
(1) |
Boys
(2) |
(3) |
| Before |
5 u |
2 u |
2 u |
| Change |
- 19 |
+ 13 |
+ 13 + 13 = + 26 |
| After |
5 u |
2 u + 13 |
2 u + 26 |
Comparing girls and
boys in the end |
13 more |
|
|
Since the number of girls is 13 more than the number of boys in the end, when we
add 13 to (2) to form (3), the number of girls and boys in the end will be the same.
(1) = (3)
5 u - 19 = 2 u + 26
5 u - 2 u = 26 + 19
3 u = 45
1 u = 45 ÷ 3 = 15
Number of pupils at first
= 5 u + 2 u
= 7 u
= 7 x 15
= 105
Answer(s): 105
