Question

house has a front yard with an area of 4,200 ft.2 . The area of the house plus the area of the yard is 8 times the area of the house alone. What equation does this real-world situation model? Use A for the area of the house.(

Answer 1

Let's denote the area of the house as \( A \) (in square feet).

According to the problem:

1. The area of the front yard is given as \( 4,200 \, \text{ft}^2 \).
2. The total area of the house plus the yard is given to be 8 times the area of the house.

The total area of the house plus the yard can be expressed as:
\[
A + 4,200
\]

According to the information given, this total area is equal to 8 times the area of the house:
\[
A + 4,200 = 8A
\]

To express this in a standard form, we can rearrange the equation by isolating \( A \):
\[
4,200 = 8A - A
\]
\[
4,200 = 7A
\]

So, the equation modeling this situation is:
\[
A + 4,200 = 8A
\]

or equivalently,
\[
4,200 = 7A
\]

Both of these equations accurately represent the given real-world scenario.