My square orchid garden abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $5 per foot, and the fencing for the east and west sides costs $1 per foot. Find the total cost of the fencing as a function of the length (in feet) of a side *x*.

To find the total cost of the fencing as a function of the length of a side, $ x $, let's break down the problem step by step.

1. **Orchid Garden Shape and Boundaries**: The orchid garden is square-shaped with side length $ x $, and it abuts the house on the northern side. Therefore, fencing is only required for the southern, eastern, and western sides.

2. **Fencing Costs**:
   - Southern side: The length of the southern boundary is $ x $, and the cost per foot is $5.
   - Eastern side: The length of the eastern boundary is $ x $, and the cost per foot is $1.
   - Western side: The length of the western boundary is $ x $, and the cost per foot is $1.

3. **Total Cost Calculation**:
   - Cost for the southern side: $ 5x $ dollars (since it's $5 per foot).
   - Cost for the eastern side: $ 1x $ dollars (since it's $1 per foot).
   - Cost for the western side: $ 1x $ dollars (since it's $1 per foot).

4. **Total Fencing Cost**: 
   The total cost is the sum of the costs for the southern, eastern, and western sides:
   \[
   \text{Total Cost} = 5x + 1x + 1x = 7x
   \]
   
Thus, the total cost of the fencing as a function of $ x $, the length of the side of the square, is:
\[
C(x) = 7x
\]

### Do you want more details or have any questions?

Here are some related questions to explore:
1. What is the cost for a garden with side length 20 feet?
2. How does the cost change if the southern side costs $10 per foot instead?
3. How would the function change if fencing was also required for the northern side?
4. What happens to the total cost if the length of the side doubles?
5. How does the function change if the cost of the east and west sides rises to $2 per foot?

**Tip**: Always start by identifying which sides require fencing and what the cost is for each boundary.

My square orchid garden abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $5 per foot, and the fencing for the east and west sides costs $1 per foot. Find the total cost of the fencing as a function of the length (in feet) of a side x.

Learn how to calculate the total cost of fencing for a square orchid garden abutting a house where the southern boundary costs $5 per foot and the east and west boundaries cost $1 per foot. Understand the linear function that represents the cost as a function of the garden side length. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation