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62. Business and finance. 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?

2007-06-12 06:30:26 · 7 answers · asked by Anonymous in Science & Mathematics Mathematics

7 answers

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

F + P = 850..................................this eqn represents counts
(300)F + (225)P = 217500.........this eqn represents costs

F = 850 - P.......................solve for F in terms of P and sub in

(300)(850 - P) + (225)P = 217500
255000 - 300P +225P = 217500
255000 -75P = 217500
75P = 255000 - 217500 = 37500

P = 37500/75 = 500 pine trees
F = 850 - P = 8500 - 500 = 350 fir trees

2007-06-12 06:40:33 · answer #1 · answered by MamaMia © 7 · 1 1

Fir trees = 350
Pine trees = 500


Fir trees + Pine trees = 850
Fir trees * $300 + Pine trees * $225 = $217,500

Two equations, two variables. Multiply the first by $300 on each side: $300 * Fir + $300 * Pine = $300 * 850 = $255,000. Then subtract the left side of the second equation from the left side of this one and do the same with the right sides: $300*Fir - $300*Fir + $300*Pine - $225*Pine = $255,000 - $217,500 so: $75*Pine = $37,500. Divide each side by $75: $75*Pine/$75 = $37,500/$75 so: Pine trees = 500.

Then using the initial equation: Fir trees + Pine trees = 850, we get: Fir trees + 500 = 850 and that resolves to: Fir trees = 350.

2007-06-12 06:46:25 · answer #2 · answered by roynburton 5 · 0 0

300 D +225 P = 217.500
Dividing by 75 which is the MCD of 300 and 225 we get
4D+3P=2900 so the equation has solutions
To solve this diophantic equation
P=966-D+(150-75D)/225
call (150-75D)/225=x so
D=2-3x x integer
2-3x<850 3x>-848 x>=-282
P=966-2+3x+x =964+4x <850 so x <=-29
For x= -29 we get
D=89 and P =848 but there are 282--29 solutions
If the problems means that
D+P=850
4D+3P= 2900 so P=850-D and 4D-3D+2550= 2900
so
D=350 and P=500

2007-06-12 07:33:01 · answer #3 · answered by santmann2002 7 · 0 0

allow the Douglas Firs = x and the Pine trees = y

x+y=850
300x+225y=217,500

Take the first equation and set it equal to "x"
x=850-y

Sub this in for "x" in the second equation and solve for "y"
300(850-y)+225y=217,500
255,000-300y+225y=217,500
-75y=-37,500
y=500

Now that you know that y=500 sub back into the first equation
x+500=850
x=350

So therefore, there were 350 Dougs and 500 Pines

2007-06-12 06:44:25 · answer #4 · answered by Jonathan C 1 · 1 0

You have to set up two simultaneous equations.
Let D = no of Douglas fir trees
P = no of other kind

So D + P = 850
300D + 225P = 217500

Now you have to solve those equations. You'll get
D = 350, P = 500

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2016-11-23 14:22:07 · answer #6 · answered by Anonymous · 0 0

Form two equations and solve simultaneously:
x + y = 850
300x + 225y = 217500

2007-06-12 06:38:10 · answer #7 · answered by Daniel A 2 · 2 1

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