A house has a front yard with an area of 4,200ft.^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 \( A \) represent the area of the house. According to the problem, the area of the front yard is given as 4,200 ft².

The total area of the house plus the area of the yard is expressed as:

\[ A + 4200 \]

The problem states that this total area is 8 times the area of the house alone. Therefore, we can set up the following equation:

\[ A + 4200 = 8A \]

This equation models the real-world situation described. You can simplify it to solve for \( A \):

\[ 4200 = 8A - A \] \[ 4200 = 7A \] \[ A = \frac{4200}{7} \] \[ A = 600 \]

So, the area of the house is 600 ft². The equation that models the real-world situation is:

\[ A + 4200 = 8A \]