Question

A nursery has $45,000 of inventory in dogwood trees and red maple trees. the profit on a dogwood tree is 26% and the profit on a red maple tree is 17%. the profit for the entire stock is 20%. how much was invested in each type of tree?

Answer 1

Dogwood cost = $15000 Red Maple cost = $30000 First, write an expression expressing what you know. x = percent of inventory that's dogwood trees (1-x) = percent of inventory that's red maple trees So the expression looks like 0.26x + 0.17(1-x) = 0.20 Solve for x. Distribute the 0.17 0.26x + 0.17 - 0.17x = 0.20 Merge the x terms 0.09x + 0.17 = 0.20 Subtract 0.17 from both sides 0.09x = 0.20 - 0.17 = 0.03 Divide by 0.09 on both sides x = 1/3 So one third of the inventory cost is dogwoods and two thirds is red maples. So Dogwood cost = 45000 * 1/3 = $15000 Red Maple cost = 45000 * 2/3 = $30000