A nursery has $40,000 of inventory in dogwood trees and red maple trees. the profit on a dogwood tree is 27% and the profit on a red maple tree is 19%. the profit for the entire stock is 20%. how much was invested in each type of tree?

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Rupicapra Rupicapra · Answer 1 · 2018-10-11T07:53:27+02:00

Answer: The amount invested in the dogwood tree was $5000, while $35000 was invested in the red maple tree.

We arrive at the answer as follows:

Let the proportion of dogwood trees be x.

Then the proportion of red maple trees in the nursery will be 1-x, since there are only two types of trees in the nursery.

We use the following formula to find the proportion dogwood and maple trees in the nursery:

[tex]20 = 27x + 19(1-x)[/tex]

Solving for x we get

[tex]20 = 27x + 19 - 19x[/tex]

[tex]x = \frac{1}{8}[/tex]

We can find the proportion of maple trees as follows:

[tex]1 - \frac{1}{8} = \frac{7}{8}[/tex]

Since we have the proportions, we can easily find the amount invested in type of tree as follows:

[tex]Dogwood = 40000*\frac{1}{8} = 5000[/tex]

[tex]Red Maple tree = 40000*\frac{7}{8} = 35000[/tex]