Ask Question
3 August, 15:27

A nursery has two hundred 7-gallon palm trees to sell, consisting of coconut palm trees, saw palmetto palm trees and christmas palm trees. Coconut palm trees sell for $75 each, saw palmetto palm trees sell for $45 each, and christmas palm trees sell for $30 each. The nursery has three times as many saw palmetto palm trees as christmas palm trees. A developer purchases all of the nursery's palm trees for a total price of 12,300. How many of each type of palm tree does the developer purchase?

+4
Answers (1)
  1. 3 August, 17:42
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A nursery has two hundred 7-gallon palm trees to sell, consisting of coconut palm trees, saw palmetto palm trees and christmas palm trees. ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers