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A nursery has $50,000 of inventory in dogwood trees and red maple trees. The profit on a dogwood tree is 24%, and the profit on a red maple tree is 10%. The profit for the entire stock is 17%. How much was invested in each type of tree?

Answer :

Using elimination method, The nursery has invested $25,000 in both dogwood trees and red maple trees, with each type of tree accounting for half of the $50,000 total inventory, given their respective profit percentages, resulting in a total profit of $8,500.

How much was invested in each type of tree?

Let's call the amount invested in dogwood trees "D" dollars and the amount invested in red maple trees "R" dollars.

We know that the total inventory is $50,000, so we can write the equation:

D + R = $50,000

Now, let's calculate the profit from each type of tree:

- The profit from dogwood trees is 24% of the amount invested in dogwood trees, which is 0.24D dollars.

- The profit from red maple trees is 10% of the amount invested in red maple trees, which is 0.10R dollars.

The total profit for the entire stock is 17% of the total inventory, which is 0.17 * $50,000 = $8,500.

So, we can write another equation for the total profit:

0.24D + 0.10R = $8,500

Now, we have a system of two equations:

1. D + R = $50,000

2. 0.24D + 0.10R = $8,500

We can solve this system of equations to find the values of D and R.

First, let's simplify the second equation by multiplying both sides by 100 to get rid of the decimals:

24D + 10R = $850,000

Now, we can use the method of substitution or elimination to solve for D and R. Let's use the elimination method. Multiply the first equation by 24 to match the coefficients of D in both equations:

24D + 24R = $1,200,000 (multiply the first equation by 24)

Now, subtract the second equation from the first:

(24D + 24R) - (24D + 10R) = $1,200,000 - $850,000

14R = $350,000

Now, divide both sides by 14 to solve for R:

R = $350,000 / 14

R = $25,000

Now that we have the value of R, we can substitute it back into the first equation to find D:

D + $25,000 = $50,000

Subtract $25,000 from both sides:

D = $50,000 - $25,000

D = $25,000

So, the nursery has invested $25,000 in dogwood trees and $25,000 in red maple trees.

Learn more on elimination method here;

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