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

Answer 1

Let's denote the area of the house as \( H \) and the area of the yard as \( Y \).

From the information given, we have two key pieces of information:

1. The area of the yard: \( Y = 4,200 \) ft².
2. The total area of the house plus the yard is 8 times the area of the house alone:

\[
H + Y = 8H
\]

Now, substituting the value of \( Y \) into the second equation gives:

\[
H + 4,200 = 8H
\]

To simplify this equation, we can rearrange it:

\[
4,200 = 8H - H
\]

\[
4,200 = 7H
\]

Now, we can express this in equation form. The equation that models the relationship between the area of the house and the area of the yard, based on the information provided, is:

\[
H + 4,200 = 8H
\]

This equation links the area of the house to the known area of the yard and illustrates that the total area is dependent on the area of the house.