Question

an orchard has 360 pear trees. the number of rows exceeds the number of trees per row by 2. how many trees are there in each row?

Explanation:

Define variables and set up equation

Let \(x\) represent the number of trees per row.
The number of rows exceeds the number of trees per row by 2, so the number of rows is \(x + 2\).
The total number of trees is 360:

$$x(x + 2) = 360$$

Write in standard form

Using the Standard Form of Quadratic Equations knowledge point

$$
LATEXBLOCK0
$$

Factor the quadratic equation

Using the Factoring Quadratic Equations knowledge point

$$
LATEXBLOCK1
$$

Solve for x

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK2
$$

Since the number of trees per row must be positive, we choose \(x = 18\).

Answer:

An orchard has 360 pear trees. The number of rows exceeds the number of trees per row by 2. How many trees are there in each row? <blank>18</blank> trees