Question

1. the larson family are planning their new house. it is going to be 25 ft on one side and have a garage that is 15 ft wide, but they have not decided on the length of the house yet.

a. if the total area of the house + garage is limited to 1200 square feet, how long can the house be?
b. write a single equation for the question above. write it in the form “(formula for area) = 1200.” you do not have to solve the equation—just write it.
we can even model expressions with subtraction, such as 3(7 - 2), using an area model. we use dark shading to indicate that an area is subtracted (
egative\ area).
for example, the picture above illustrates 3(7 - 2)=3·7 - 3·2.
a. what expression is modeled below?
b. draw a model for 3(x + y - 2)=3x + 3y - 6.

Explanation:

16a

Step1: Calculate total width

The total width of the house - garage combination is $15 + x$ feet, and the length is 25 feet. The area formula for a rectangle is $A = length\times width$.

Step2: Set up area - equation

We know that $A = 1200$ square feet, and $A=25\times(15 + x)$. So, $1200=25\times(15 + x)$. First, divide both sides of the equation by 25: $\frac{1200}{25}=15 + x$.

Step3: Solve for $x$

Since $\frac{1200}{25}=48$, the equation becomes $48 = 15+x$. Then subtract 15 from both sides: $x=48 - 15$.

The rectangle has a length of $y$ and a width of 5. The non - shaded part has a length of $y - 9$. Using the area model and the distributive property, the area of the whole rectangle is $5y$ and the area of the non - shaded part is $5\times9$.

Answer:

$x = 33$ feet

16b