Aschool district needs 3 teachers for every 70 children. they expect to have 14,700 children in the district next year. at this time, they have 612 teachers. how many more teachers are needed?

They need 18 more teachers.
Set the problem up as a ratio.
 3           x
  = 
70       14,700

70 x = 44,100
     x = 630

The district already has 612 teachers. So, 630 - 612 = 18 more needed.

There are several information's already given in the question. Let us focus on them to get to the answer.
For every 70 children, the number of teachers required = 3
Then
For every 14700 children, the
number of teachers required = (3 * 14700)/70
                                              = 630
The number of teachers in school now = 612
Number of more teachers required = 618 - 612
                                                        = 6
So 6 more teachers are required in the school.