Answer:
350 Douglas fir, 500 Ponderosa pine
Step-by-step explanation:
  Let f = the number of fir trees
and p = the number of pine trees.
Then, we have two conditions:
(1)                                f + p = 850
(2)                  300f + 225p = 217 500
(3)                                    p = 850 -f         Subtracted f from each side of (1)
(4)       300f + 225(850 - f) = 217 500     Substituted (3) into (3)
       300f + 191 250 - 225f = 217 500     Distributed 225
                     75f + 191 250 = 217 500     Distributed the 7
                                     75f = 26 250      Subtracted 191 250 each side
(5)                                     f = 350
                              350 + p = 850           Substituted (5) into (1)
                                         p = 500          Subtracted 350 from each side
The company bought 350 fir trees and 500 pine trees.
Check:
(1) 350 + 500 = 850     (2) 300 × 350 + 225 × 500 = 217 500  
               850 = 850                  105 000 + 112 500 = 217 500
                                                                    217 500 = 217 500
OK.