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