The ratio of the boys to the girls in a school was 8 : 5. After 17 boys went home and 21 new girls came, there were 10 more boys than girls in the end. Find the number of children in the school in the end.
| |
Boys
(1) |
Girls
(2) |
(3) |
| Before |
8 u |
5 u |
5 u |
| Change |
- 17 |
+ 21 |
+ 21 + 10 = + 31 |
| After |
8 u |
5 u + 21 |
5 u + 31 |
Comparing boys and
girls in the end |
10 more |
|
|
Since the number of boys is 10 more than the number of girls in the end, when we
add 10 to (2) to form (3), the number of boys and girls in the end will be the same.
(1) = (3)
8 u - 17 = 5 u + 31
8 u - 5 u = 31 + 17
3 u = 48
1 u = 48 ÷ 3 = 16
Number of children in the end
= 8 u + 5 u - 17 + 21
= 13 u + 4
= 13 x 16 + 4
= 208 + 4
= 212
Answer(s): 212
