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There are 850 Douglas fir and Ponderosa pine trees in a section of forest bought by Karamazov Logging Co. The company paid an average of $300 for each Douglas fir and $225 for each Ponderosa pine. if the company paid $217.500 for the trees, how many of each kind did the company buy?

Respuesta :

znk

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.

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