Question

A house has a front yard with area of 4,200 ft squared area of the house plus area of the yard is 8 times the area of the house alone. What equation does this real world model. Use A for area of the house

Answer 1

Let \( A \) represent the area of the house in square feet. The area of the front yard is given as 4,200 square feet.

According to the problem, the total area of the house plus the area of the yard is eight times the area of the house alone. We can express this mathematically as:

\[
\text{Area of the house} + \text{Area of the yard} = 8 \times \text{Area of the house}
\]

Substituting in the values we have:

\[
A + 4200 = 8A
\]

Now, you can rearrange this equation to isolate \( A \):

1. Subtract \( A \) from both sides:
\[
4200 = 8A - A
\]
\[
4200 = 7A
\]

2. Divide both sides by 7:
\[
A = \frac{4200}{7}
\]
\[
A = 600
\]

Thus, the area of the house is 600 square feet. The equation that represents the relationship between the area of the house and the yard is:

\[
A + 4200 = 8A
\]

Or equivalently, you can express it in a simpler form:

\[
7A = 4200
\]

This simplifies the relationship effectively for solving for \( A \).