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Question

There are 850 Douglas fir and ponderosa pine trees in a
section of forest bought by Sawz 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?

Answer 1

Two equations and two unknowns:

Let F = number of fir trees
Let P = number of pine trees

F + P = 850
300 * F + 225 * P = 217,500

Start by solving for one of the variables:
F = 850 - P

Then substitute that into the second equation:
300 * (850 - P) + 225 P = 217500

Distribute the 300 through the parentheses:
255000 - 300 P + 225 P = 217500

Add the P terms:
255000 - 75P = 217500

Add 75P to both sides:
255000 = 217500 + 75P

Subtract 217500 from both sides:
37500 = 75P

Divide both sides by 75
P = 500

From there you can easily solve for F:
F = 850 - P
F = 850 - 500
F = 350

So they bought 350 Douglas Firs and 500 Ponderosa Pines.

Answer 2

Ok convert it to algebra
let x = number of douglas firs
let y = number of ponderosa pine

"There are 850 Douglas fir and ponderosa pine trees in a
section of forest bought by Sawz Logging Co."

So that means x + y = 850

"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?"

That means 300x + 225y = 217500

so we have
x + y = 850
300x + 225y = 217500

Let's multiply both sides of the first problem by 300 to get rid of the xs

300 * (x+y) = 300 * 850

300x + 300y = 255000
300x + 225y = 217500

subtract the 2nd equation from the first

0x + 75y = 37500
75y = 37500 ---- divide both sides by 75

y = 500

Now substitute 500 for y in the original 1st problem

x + y = 850
x + 500 = 850 --- subtract 500 from each side
x = 350

So the company bought 350 Douglas Fir Trees and 500 Ponderosa Pines

Answer 3

let

x = ponderosa pine

y = Douglas fie

850 = Total trees

225x = cost os each ponderosa tree

300y = cost of each Douglas fir

217500 = total cost of the trees

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x + y = 850- - - - - - - - - -Equation 1
225x + 30y = 217500- - - Equation 2
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Substitution Method equation 1

x + y = 850

x + y - x = 850 - x

y = 850 - x

The answer is y = 850 - x

Insert the y value into equation 2

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225x + 300y = 217500

225x + 300(850 - x) = 217500

225x + 255000 - 300x = 217500

- 75x + 255000 = 217500

- 75x + 255000 - 255000 = 217500 - 255000

- 75x = - 37500

- 75x / - 75 = - 37500 / - 75

x = 500

The answer is x = 500

Insert the x value into equation 1

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x + y = 850

500 + y = 850

500 + y - 500 = 850 - 500

y = 350

The answer is y = 350

Insert the y value into equation 1

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Check for equation 1

x + y = 850

500 + 350 = 850

850 = 850

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Check for equation 2

225x + 300y = 217500

225(500) + 300(350) = 217500

112500 + 105000 = 217500

217500 = 217500

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The company purchased 500 Ponderosa Pines

The company purchased 350 Douglas firs

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The solution set { 500, 350 }

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