Given the equation 8(n+6)=104

Question

, identify the real-world problem that corresponds to this equation.(1 point)
Responses

1.A rectangle of is divided into two sections. One section has a length of n and a width of 6 comprised of a 2 by 4 matrix of square boxes. The second section has a length of 8 and a width of 6 comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: upper A equals 104 square units.
Image with alt text: A rectangle of is divided into two sections. One section has a length of n and a width of 6 comprised of a 2 by 4 matrix of square boxes. The second section has a length of 8 and a width of 6 comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: upper A equals 104 square units.

2.A rectangle is divided into two sections. One section has a length of 8 and a width of n comprised of a 2 by 4 matrix of square boxes. The second section has a width of n plus 6 and length of 8 comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: upper A equals 104 square units.
Image with alt text: A rectangle is divided into two sections. One section has a length of 8 and a width of n comprised of a 2 by 4 matrix of square boxes. The second section has a width of n plus 6 and length of 8 comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: upper A equals 104 square units.

3.A rectangle is divided into two sections. One section has a length of n minus 6 and width 8 comprised of a 2 by 4 matrix of square boxes. The second section has a length of n and width of 8 comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: upper A equals 104 square units.
Image with alt text: A rectangle is divided into two sections. One section has a length of n minus 6 and width 8 comprised of a 2 by 4 matrix of square boxes. The second section has a length of n and width of 8 comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: upper A equals 104 square units.

4.A rectangle is divided into two sections. One section has a length of 8 and width of 6 comprised of a 2 by 4 matrix of square boxes. The second section has a length of 8 and width of n comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: upper A equals 104 square units.

Answer 1

To solve the equation \(8(n+6)=104\), we need to understand the real-world scenario it represents.

The equation \(8(n+6)=104\) implies that the total area of a rectangle is \(104\) square units. The length of one section of the rectangle is \(8\), while the width of that section is expressed as \(n + 6\).

Let's evaluate the options you provided:

1. Option 1: This scenario suggests a section has a length of \(n\) and a width of \(6\), which does not match the equation's structure.

2. Option 2: This describes one section having a width of \(n + 6\) with a length of \(8\), which perfectly corresponds to \(8(n + 6)\) for the area of that section. The other section does not match the initial equation though.

3. Option 3: This describes sections with dimensions different from those in the equation.

4. Option 4: This describes one section with a width of \(n\) and a dimension that doesn't match what's given in the equation.

The best match for the equation \(8(n + 6) = 104\) is Option 2, which has the correct dimensions for the area calculation based on the rearrangement of the given equation.

Thus, the answer is 2.