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?

Three teachers are needed for 70 children, that is:
3 = 70  equation 1.
 For 14,700 children, Y number of teachers are needed, thus, we have
Y = 14,700equation 2.
3 = 70
Y = 14, 700.
Cross multiplying we give us,
3 * 14, 700/70 * Y.
44,100/70Y
Y = 630.
Thus, 630 teachers are needed to teach 14,700 children.
The district already have 612 teachers, so they need 630 - 612 = 18. 
So, the district needs 18 more teachers.

What am i doing here. add?