[( m - 3 ) / 5] + [(m - 4 ) / 7] = 6 - [(2m - 1) / 35]

m = 18

Step-by-step explanation:

It took a while but I have the steps too. Don't know if I'm seeing your equation wrong but I tried.

You want to replace the s with 150 in the equation and then just solve for t.
150=16√7t +62    subtract 62 from both sides
88=16√7t              divide both sides by 16
5.5=√7t                to get rid of the square root  square both sides. 
30.25=7t              now divide both sides by 7
4.3 = t (approximately) 
so at 4 weeks they will have sold 150 units.