Total number of trees available to be sold = 200
Selling price of coconut palm trees sell (Pco)= $75 each
Selling price of saw palmetto palm trees sell (Pp) = $45 each
Selling price of christmas palm trees (Pch) = $30 each
Number of saw palmetto palm trees (Np) = 3 × Number of christmas palm trees (Nch)
Let number of coconut palm trees be Nco
Total price paid by developer for all the palm trees = 12,300
So Total number of trees = Nco + Np + Nch
⇒ 200 = Nco + 3×Nch + Nch
⇒ 200 = Nco + 4Nch ................ (i)
Total selling price of trees = Sco × Nco + Sp × Np + Sch × Nch
⇒ 12,300 = 75×Nco + 45×Np + 30×Nch
Dividing above equation by 5
⇒ 2,460 = 15Nco + 9Np + 6Nch
Substituting Np = 3Nch in the above equation
⇒ 2,460 = 15Nco + 9 (3Nch) + 6Nch
⇒ 2,460 = 15Nco + 33Nch ................ (ii)
Mutiply (i) with 15 and subtract from (ii)
⇒ 2,460 - 3,000 = 15Nco + 33Nch - 15Nco - 60Nch
⇒ -540 = 33Nch - 60Nch
⇒ -540 = 27Nch
⇒ Nch=20
If Nch = 20, Np = 3×20 = 60
Since Nco + Np + Nch = 200
⇒ Nco = 200 - (80)
⇒ Nco = 120
Hence, the developer purchased 120 coconut palm trees, 20 christmas palm trees and 60 saw palmetto palm trees.
