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 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.

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 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.

GPT-4o mini · Answer

To solve the equation $ 8(n + 6) = 104 $, we can analyze its components in the context of the given choices. 1. **Understanding the equation**: The equation represents the area of a rectangle that is composed of two sections. Here, $ 8 $ represents the common length of both sections (which remains constant), and $ n + 6 $ indicates the varying width of one section, while the other has a width represented by $ n $. 2. **Real-world context**: In the context of the problem, we would have a rectangle where one section has a width of $ n + 6 $ (the first section) and the area of this section is equal to the height (8) times the width ($ n + 6 $). The total area of both sections must equal 104 square units. Based on the analysis, the option that best describes the scenario represented by the equation $ 8(n + 6) = 104 $ 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 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."** Thus, the correct response would be the second option in your list.