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
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answer #1
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answered by MamaMia © 7
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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
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answer #2
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answered by roynburton 5
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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
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answer #3
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answered by santmann2002 7
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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
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answer #4
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answered by Jonathan C 1
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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
2007-06-12 06:40:17
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answer #5
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answered by Dr D 7
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2016-11-23 14:22:07
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answer #6
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answered by Anonymous
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Form two equations and solve simultaneously:
x + y = 850
300x + 225y = 217500
2007-06-12 06:38:10
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answer #7
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answered by Daniel A 2
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