Answer :
To solve the problem, we need to find what number makes the given statement true. Let's break down the solution step-by-step:
1. Understand the problem:
- We are given that the product of 8 and the sum of 4 and a number is 112.
- We need to find the unknown number.
2. Translate the problem into an equation:
- The words "the sum of 4 and a number" can be represented as [tex]\(4 + n\)[/tex], where [tex]\(n\)[/tex] is the unknown number.
- "The product of 8 and the sum" means we multiply 8 by [tex]\(4 + n\)[/tex].
- The equation that describes this relationship is [tex]\(8(4 + n) = 112\)[/tex].
3. Set up and solve the equation:
- Start with the equation: [tex]\(8(4 + n) = 112\)[/tex].
- Distribute the 8: [tex]\(8 \times 4 + 8 \times n = 112\)[/tex].
- This simplifies to: [tex]\(32 + 8n = 112\)[/tex].
4. Isolate the variable:
- Subtract 32 from both sides to get: [tex]\(8n = 112 - 32\)[/tex].
- Simplifying this gives: [tex]\(8n = 80\)[/tex].
5. Solve for [tex]\(n\)[/tex]:
- Divide both sides by 8 to isolate [tex]\(n\)[/tex]: [tex]\(n = 80 / 8\)[/tex].
- Simplifying this results in: [tex]\(n = 10\)[/tex].
So, the number is 10.
The correct equation you can use to solve for the number is [tex]\(8(4+n)=112\)[/tex].
1. Understand the problem:
- We are given that the product of 8 and the sum of 4 and a number is 112.
- We need to find the unknown number.
2. Translate the problem into an equation:
- The words "the sum of 4 and a number" can be represented as [tex]\(4 + n\)[/tex], where [tex]\(n\)[/tex] is the unknown number.
- "The product of 8 and the sum" means we multiply 8 by [tex]\(4 + n\)[/tex].
- The equation that describes this relationship is [tex]\(8(4 + n) = 112\)[/tex].
3. Set up and solve the equation:
- Start with the equation: [tex]\(8(4 + n) = 112\)[/tex].
- Distribute the 8: [tex]\(8 \times 4 + 8 \times n = 112\)[/tex].
- This simplifies to: [tex]\(32 + 8n = 112\)[/tex].
4. Isolate the variable:
- Subtract 32 from both sides to get: [tex]\(8n = 112 - 32\)[/tex].
- Simplifying this gives: [tex]\(8n = 80\)[/tex].
5. Solve for [tex]\(n\)[/tex]:
- Divide both sides by 8 to isolate [tex]\(n\)[/tex]: [tex]\(n = 80 / 8\)[/tex].
- Simplifying this results in: [tex]\(n = 10\)[/tex].
So, the number is 10.
The correct equation you can use to solve for the number is [tex]\(8(4+n)=112\)[/tex].
