Problem Solving with Multi-Step Equations Quick Check

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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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To identify the real-world problem that corresponds to the given equation, we need to understand the equation and its meaning. The equation is 8(n+6) = 104.

To solve this equation, we can follow the steps below:

Step 1: Distribute the 8 to n+6:
8n + 48 = 104

Step 2: Subtract 48 from both sides of the equation:
8n = 104 - 48
8n = 56

Step 3: Divide both sides of the equation by 8:
n = 56 / 8
n = 7

Therefore, the solution to the equation is n = 7.

Now let's analyze the answer choices to identify the real-world problem that corresponds to this equation.

Option A: A rectangle 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: A = 104 square units.

Option B: A rectangle is divided into two sections. One section has a length of n-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: A = 104 square units.

Option C: 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 a length of 8 comprised of a 3 by 4 matrix of square boxes. Above the rectangle, it reads: A = 104 square units.

Option D: A rectangle is divided into two sections. One section has a length of 8 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 n comprised of a 3 by 4 matrix of square boxes. Above the rectangle it reads: A = 104 square units.

Analyzing the options, we can see that option C accurately describes the real-world problem that corresponds to the equation. It states that a rectangle is divided into two sections, one with a length of 8 and a width of n and the other with a width of n+6 and a length of 8. The total area of the rectangle is 104 square units.

Therefore, the correct answer is option C.