Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

A student government organization is selling Christmas trees as a fundraiser. On Friday, they sold 5 noble fir trees and 3 douglas fir trees for a total of $420. On Saturday, 12 noble fir trees and 9 douglas fir trees were sold for a total of $1,080. What is the cost per tree for each type?

Sagot :

collinse
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

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.

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.