Problem Solving with Multi-Step Equations Quick Check
2 of 52 of 5 Items
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.
Skip to navigation
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.