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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 :

Matheng

Answer:

The number of Douglas fir trees = 350

The number of Ponderosa pine trees = 500

Step-by-step explanation:

Let the number of Douglas fir trees = x

Let the number of Ponderosa pine trees = y

There are 850 Douglas fir and Ponderosa pine trees.

x + y = 850

y = 850 - x   ⇒(1)

The company paid an average of $300 for each Douglas fir and $225 for each Ponderosa pine, and the company paid $217,500 for the trees.

300 x + 225 y = 217,500 ⇒(2)

substitute from (1) at (2)

300x + 225 (850 - x) = 217,500

Solve for x

300x + 225 * 850 - 225x = 217,500

300x - 225x = 217,500 - 225*850

75x = 26,250

x = 26,250/75 = 350

y = 850 - 350 = 500

So,

The number of Douglas fir trees = 350

The number of Ponderosa pine trees = 500