The Problem:

In a garden, trees are planted in horizontal and vertical rows. There are 4 rows more in each horizontal row than in a vertical row. In total, there are 480 trees. We need to find the number of trees in each horizontal row.

Given:

- The number of horizontal rows is 4 more than the number of vertical rows.
- The total number of trees is 480.

Approach:

To solve this problem, we can use algebraic equations. Let's assume the number of trees in a vertical row is "x". Since there are 4 more horizontal rows than vertical rows, the number of trees in a horizontal row would be "x + 4".

The Solution:

Let's break down the problem into smaller steps:

Step 1: Set up the equations based on the given information.

Let "x" be the number of trees in a vertical row.
Therefore, the number of trees in a horizontal row would be "x + 4".

The total number of trees can be calculated using the formula:
Total number of trees = Number of vertical rows * Number of trees in a vertical row

Given that there are 480 trees in total, we can write:
480 = Number of vertical rows * x

Step 2: Solve the equation.

Now, we have two equations:
480 = Number of vertical rows * x
Number of trees in a horizontal row = x + 4

Step 3: Substitute the value of "x" from the first equation into the second equation.

480 = Number of vertical rows * x
480 = Number of vertical rows * (Number of trees in a horizontal row - 4)

Step 4: Simplify the equation.

480 = Number of vertical rows * (Number of trees in a horizontal row - 4)

Since there are 4 more horizontal rows than vertical rows, we can rewrite the equation as:
480 = (Number of vertical rows + 4) * (Number of vertical rows)

Step 5: Solve for the number of vertical rows.

480 = (Number of vertical rows + 4) * (Number of vertical rows)
480 = Number of vertical rows^2 + 4 * Number of vertical rows

Step 6: Rewrite the equation in the standard quadratic form.

Number of vertical rows^2 + 4 * Number of vertical rows - 480 = 0

Step 7: Factorize the equation.

(Number of vertical rows + 24) * (Number of vertical rows - 20) = 0

Step 8: Find the possible values for the number of vertical rows.

From the equation, we get two possible values for the number of vertical rows:
- Number of vertical rows + 24 = 0 --> Number of vertical rows = -24 (Not possible as the number of rows cannot be negative)
- Number of vertical rows - 20 = 0 --> Number of vertical rows = 20

Step 9: Substitute the value of the number of vertical rows into the equation for the number of trees in a horizontal row.

Number of trees in a horizontal row = Number of vertical rows + 4

Substituting the value of