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.(

1 answer

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.