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8 Set up a system and solve. Dr. McCarty has decided that she wants to plant eight new trees in her yard. Oak trees are $18.99 (including tax ) each, and dogwood trees are 23.87 each (including tax ). She spent a total of $166.56 on the trees.

Answer :

Final answer:

To solve this problem, we set up a system of linear equations based on the information given. The number of Oak trees is represented by x and the number of Dogwood trees by y. The solution to the system's equations is x = 4 and y = 4, which means Dr. McCarty bought 4 Oak trees and 4 Dogwood trees.

Explanation:

Let's define the number of Oak trees as x and the number of Dogwood trees as y. We already know that Dr. McCarty wants to plant 8 trees, so the first equation is x + y = 8. We also know that she spent a total of $166.56, so the second equation is 18.99x + 23.87y = 166.56. These two equations form a system of linear equations that can be solved simultaneously. To solve the system, you can use substitution or elimination method.

For simplicity, let's use the substitution method:

  1. Solve the first equation for x: x = 8 - y.
  2. Substitute x in the second equation: 18.99(8 - y) + 23.87y = 166.56.
  3. Simplify and solve for y: y = 4.
  4. Substitute y = 4 in the first equation to find x: x = 8 - 4 = 4.

The solution to the system's equations is x = 4 and y = 4, meaning Dr. McCarty bought 4 Oak trees and 4 Dogwood trees.

Learn more about Solving system of equations here:

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