Thank you for visiting A nursery has 60 000 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:
By setting up a system of equations with the given investment and profit percentages for dogwood trees and red maple trees, and solving it, we can deduce that the nursery invested $15,000 in dogwood trees and $45,000 in red maple trees.
Explanation:
To solve this problem, we can set up a system of equations to represent the investments in dogwood trees and red maple trees, as well as the profits made from each. Let x be the amount invested in dogwood trees and y be the amount invested in red maple trees. We know that the total investment is $60,000, so we have the first equation:
x + y = 60,000
We're also given the profit percentages for each tree type: 29% for dogwood and 17% for red maple. The overall profit is 20%, applied to the total inventory. This gives us the second equation:
0.29x + 0.17y = 0.20 × 60,000
Solving this system of equations, we have:
- x + y = 60,000
- 0.29x + 0.17y = 12,000
By solving these equations simultaneously (e.g., using substitution or elimination methods), we can find the exact investment amounts for each type of tree. To work through the details, let's use the elimination method:
- Multiply the first equation by -0.29:
- -0.29x - 0.29y = -17,400
- Now add this to the second equation:
- (-0.29x + 0.29x) + (-0.29y + 0.17y) = -17,400 + 12,000
- This simplifies to:
- -0.12y = -5,400
- Divide both sides by -0.12:
- y = 45,000
Having found y, we substitute back into the first equation to find x:
- x + 45,000 = 60,000
- x = 15,000
Thus, $15,000 was invested in dogwood trees and $45,000 in red maple trees.
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