Thank you for visiting A nursery has 55 000 of inventory in dogwood trees and red maple trees The profit on a dogwood tree is 29 and the profit. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
To determine how much was invested in each type of tree, set up a system of equations using the total inventory and profit percentages. Solve the system of equations to find the amounts invested in dogwood and red maple trees. Approximately $10,000 was invested in dogwood trees and approximately $45,000 was invested in red maple trees.
Explanation:
To solve this problem, we can set up a system of equations. Let's say x represents the amount invested in dogwood trees, and y represents the amount invested in red maple trees.
Since the nursery has a total of $55,000 in inventory, we can write the equation x + y = 55000.
We also know that the profit on a dogwood tree is 29% and the profit on a red maple tree is 18%. The profit for the entire stock is 20%. Using these percentages, we can write another equation: (0.29 * x + 0.18 * y) / (x + y) = 0.20.
Simplifying the second equation, we get 0.29x + 0.18y = 0.20(x + y).
Multiplying both sides of the equation by x + y, we get 0.29x + 0.18y = 0.20x + 0.20y.
Subtracting 0.20x and 0.18y from both sides, we have 0.09x = 0.02y.
Dividing both sides by y, we get 0.09x/y = 0.02.
Since we have two unknowns, we need another equation to solve for x and y.
Let's use the first equation x + y = 55000 to solve for x in terms of y. Subtracting y from both sides, we have x = 55000 - y.
Substituting this value of x into the third equation 0.09x/y = 0.02, we get 0.09(55000 - y)/y = 0.02.
Simplifying, we have (4950 - 0.09y) / y = 0.02.
Multiplying both sides of the equation by y, we get 4950 - 0.09y = 0.02y.
Adding 0.09y to both sides, we have 4950 = 0.11y.
Dividing both sides by 0.11, we find that y ≈ 45,000.
Substituting this value of y into the first equation x + y = 55000, we find that x ≈ 10,000.
Therefore, approximately $10,000 was invested in dogwood trees and approximately $45,000 was invested in red maple trees.
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