Question

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?
(In Dollars)

Answer 1

5 noble fir and 3 douglas fir = $ 420

12 noble fir and 9 douglas fir = $ 1080

Let noble fir be n,  and douglas fir be d.

5n + 3d = 420               ..............(i)

12n + 9d = 1080           ...............(ii)

Multiply equation (i)  by 3.

3*(5n + 3d) = 3*(420)

15n + 9d = 1260        .............(iii)

Equation (ii)  minus (iii)

(12n + 9d) - (15n + 9d) =  1080 - 1260

12n - 15n  + 9d - 9d = -180

-3n = -180

n = -180/-3 = 60

Substitute the value of n in (i)    5n + 3d = 420 

5*(60) + 3d = 420

300 + 3d  = 420
 
3d =  420 - 300 = 120

3d = 120

d = 120/3 = 40

Therefore Noble fir tree cost $60 while Douglas fir tree cost $40