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Sagot :
So you must set this up as a system of equations
n= noble fir trees
d= douglas fir trees
5n + 3d = $420
12n + 9d = $1,080
To get a positive output you have to multiply the second equation by 3 to be able to be divisable to one another
36n + 18d = 3,240
now divide the equation by 18
2n + d = 180
-2n -2n
d = 180 - 2n
Now put that equation in the first as d ^^^
5n + 3(180 -2n) = 420
5n + 540- 6n = 420
- 540 -540
1n = 120
n = 120
Now put n into the second equation( none changed one) to find d
12(120) + 9d = 3240
1440 + 9d = 3240
-1440 -1440
9d = 1800
÷9 ÷9
d= 200
so the noble is $ 120
and the douglas is $200
n= noble fir trees
d= douglas fir trees
5n + 3d = $420
12n + 9d = $1,080
To get a positive output you have to multiply the second equation by 3 to be able to be divisable to one another
36n + 18d = 3,240
now divide the equation by 18
2n + d = 180
-2n -2n
d = 180 - 2n
Now put that equation in the first as d ^^^
5n + 3(180 -2n) = 420
5n + 540- 6n = 420
- 540 -540
1n = 120
n = 120
Now put n into the second equation( none changed one) to find d
12(120) + 9d = 3240
1440 + 9d = 3240
-1440 -1440
9d = 1800
÷9 ÷9
d= 200
so the noble is $ 120
and the douglas is $200
Answer:
The cost of noble fir tree is $60.
The cost of douglas fir tree is $40.
Step-by-step explanation:
Given : A student government organization is selling Christmas trees as a fundraiser.
To find : What is the cost per tree for each type?
Solution :
Let x be the cost of noble fir tree.
and y be the cost of douglas fir tree.
On Friday, they sold 5 noble fir trees and 3 douglas fir trees for a total of $420.
i.e. [tex]5x + 3y = 420[/tex] ....(1)
On Saturday, 12 noble fir trees and 9 douglas fir trees were sold for a total of $1,080.
i.e. [tex]12x + 9y = 1080[/tex]
[tex]4x +3y =360[/tex] ......(2)
Solving equation (1) and (2),
Subtract (2) from (1),
[tex]5x + 3y-(4x +3y)= 420-360[/tex]
[tex]5x + 3y-4x-3y=60[/tex]
[tex]x=60[/tex]
Substitute in equation (1),
[tex]5(60)+ 3y = 420[/tex]
[tex]300+ 3y = 420[/tex]
[tex]3y=120[/tex]
[tex]y=40[/tex]
The cost of noble fir tree is $60.
The cost of douglas fir tree is $40.
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