Question

Jefferson's old bedroom was shaped like a rectangle. It had a length that was 5 times its width. When Jefferson's family moved, his new bedroom was also shaped like a rectangle. It was 3 feet longer and 2 feet wider than his old bedroom. If w represents the width of Jefferson's bedroom, what expression represents the difference between the area of his new bedroom and the area of his old bedroom?

Answer 1

(5w+3)(w+2)

Explanation:

5w x w = a

The new room is 3 ft longer and 2 ft wider so the new equation is

(5w+3)(w+2)

Answer 2

`\sf \textsf{Difference} = (5w + 3)(w + 2) - 5w^2`

Explanation:

Let's denote the width of Jefferson's old bedroom as
`\sf w`. Given that the length of the old bedroom is 5 times its width, the length (
`\sf l`) of the old bedroom is
`\sf 5w`.

The area (
`\sf A`) of the old bedroom is given by the product of its length and width:

`\sf A_{\textsf{old}} = l * w = (5w) * w = 5w^2`

Now, Jefferson's new bedroom is 3 feet longer and 2 feet wider than his old bedroom. Therefore, the length of the new bedroom (
`\sf L_{\textsf{new}}`) is
`\sf 5w + 3`, and the width (
`\sf W_{\textsf{new}}`) is
`\sf w + 2`.

The area (
`\sf A_{\textsf{new}}`) of the new bedroom is given by the product of its length and width:

`\sf A_{\textsf{new}} = L_{\textsf{new}} * W_{\textsf{new}} = (5w + 3) * (w + 2)`

Now, we want to find the expression that represents the difference between the area of the new bedroom and the area of the old bedroom:

`\sf \textsf{Difference} = A_{\textsf{new}} - A_{\textsf{old}}`

`\sf \textsf{Difference} = (5w + 3)(w + 2) - 5w^2`

So, the expression to represent the difference between the area of his new bedroom and the area of his old bedroom is:

`\sf \textsf{Difference} = (5w + 3)(w + 2) - 5w^2`