A nursery has $60,000 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 16%. The profit for the entire stock is 20%. How much (in dollars) was invested in each type of tree?

Red maple trees: $ _

Dogwood trees: $ _

Question

College

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Answer :

TamrynWilliams TamrynWilliams · Answer 1 · 2023-12-22T01:27:25-05:00

red maple trees: $40,000
dogwood trees: $20,000

We know the following:

Total amount invested: [tex]x + y = 60,000[/tex]
The overall profit is 20%. Therefore, the profit on the entire stock is 12,000dollars.
The profit on dogwood trees is 28%, so the profit from dogwood trees is $0.28x.
The profit on red maple trees is 16%, so the profit from red maple trees is $0.16y.
The total profit from both types of trees combined is $0.28x + 0.16y = 12,000$.

Now we have a system of linear equations:

To solve these equations, we can use the substitution method or the elimination method. Here, we'll use the substitution method.

From the first equation: [tex]y = 60,000 - x[/tex]

$0.28x + 0.16(60,000 - x) = 12,000$

Simplify the equation:

$0.28x + 9,600 - 0.16x = 12,000$

$0.12x + 9,600 = 12,000$

$0.12x = 2,400$

[tex]x = 20,000[/tex]

Now, plug the value of [tex]x[/tex] back into the first equation to find [tex]y[/tex]:

$20,000 + y = 60,000$

[tex]y = 60,000 - 20,000[/tex]

[tex]y = 40,000[/tex]

So, the amount invested in red maple trees is $40,000, and the amount invested in dogwood trees is $20,000.