a boy scout troop is selling christmas trees at a local tree lot. in the morning, they sold 20 douglas fir trees and 23 noble fir trees, earning a total of $2,417. in the afternoon, they sold 20 douglas fir trees and 18 noble fir trees, earning a total of $2,022. how much does each type of tree cost?

The cost of 1 Douglas Fir Tree = $30

The cost of 1 Noble Fir Tree = $ 79

Step-by-step explanation:

Let the cost of 1 Douglas Fir tree =  $ x

Let the cost of 1 Noble Fir tree = $ y

Total Amount Earned in morning = $2,417

Total Amount Earned in evening = $2,022

Now, according to the question:

20 x + 23 y = 2417

and 20 x + 18 y = 2022

Subtraction both equation , we get

20 x + 23 y  - (20 x + 23 y)  = 2417 - 2022

or,  20x - 20x + 23 y - 18 y  = 395

or, 5 y = 395

⇒ y = 395 / 5 =  79

Hence, the cost of 1 Noble Fir Tree = $ 79

Now, put the value of y in 20 x + 23 y = 2417 , we get

20x + 23(79) = 2417

or, 20x = 2417 - 1817 = 600

or, x  = 600/20  = 30

Hence, the cost of 1 Douglas Fir Tree = $30