Let's denote the area of the house as \( A \) (in square feet).
According to the problem:
- The area of the front yard is given as \( 4,200 , \text{ft}^2 \).
- 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.