The question is incorrect. The correct question is as follows,
A nursery has $55,000 of inventory in dogwood trees and red maple trees. The profit on a dogwood tree is 28% 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:
The investment in Dogwood trees is $15000.
The investment in red maple trees is = $40000
Explanation:
To calculate the investment in each type of tree, we will say that x was invested in dogwood trees and the investment in red maple trees was 55000-x.
The profit on the entire investment is calculated as the weighted average of the profit on dogwood trees and profit on the red maple trees. The formula for overall profit can be written as follows,
Overall profit = Investment in dogwood / total investment * profit % on dogwood + Investment in red maple / total investment * profit % on red maple
0.2 = x / 55000 * 0.28 + (55000 - x) / 55000 * 0.17
0.2 = 0.28x / 55000 + (9350 - 0.17x) / 55000
0.2 = 0.28x + 9350 - 0.17x / 55000
0.2 * 55000 = 0.11x + 9350
11000 = 0.11x + 9350
11000 - 9350 = 0.11x
1650 / 0.11 = x
x = $15000
If x is $15000, this means that the investment in Dogwood trees is $15000.
If x is $15000, this means that the investment in red maple trees is 55000 - 15000 = $40000
