Given the equation 8(n+6)=104

Question

Given the equation 8(n+6)=104
, identify the real-world problem that corresponds to this equation.(1 point)
Responses

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.

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.

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.

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. 
Image with alt text: 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.
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GPT-4o mini · Answer

To identify the correct option associated with the equation \(8(n+6)=104\), we need to analyze the components of the equation in the context of area calculation for rectangles.

Let's start by simplifying the equation:

Distributing on the left side: \(8(n + 6) = 104\) simplifies to: \(8n + 48 = 104\)
We can then isolate \(n\): \(8n = 104 - 48\) \(8n = 56\) \(n = 7\)

In the context of a real-world problem involving areas of rectangles, the left side of the equation \(8(n + 6)\) indicates that there are two sections contributing to the total area:

One section has a width of \(n + 6\) and a length of \(8\).
The total area of this section is \(8(n + 6)\).

This matches perfectly with the idea of a rectangle divided into parts, where one section has a length of \(8\) and a width of \(6\), while the other section has a width of \(n + 6\).

The corresponding real-world problem that best fits this scenario is:

"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 \(n + 6\) and length of 8 comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: \(A = 104\) square units."

Thus, the correct choice is:

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