Answer :
Sure! Let's solve the problem step by step.
We are given that the product of 8 and the sum of 4 and a number equals 112. We need to find what that number is.
1. Translate the words into an equation:
- The phrase "the sum of 4 and a number" suggests we add 4 to a number, which we can call [tex]\( n \)[/tex].
- So, 4 + [tex]\( n \)[/tex].
- The phrase "the product of 8 and" tells us we should multiply 8 by this sum.
- Therefore, we write it as: [tex]\( 8 \times (4 + n) \)[/tex].
2. Set up the equation:
- According to the problem, this product equals 112. Therefore, our equation is:
[tex]\[
8(4 + n) = 112
\][/tex]
3. Solve the equation for [tex]\( n \)[/tex]:
- Distribute the 8 to both terms inside the parenthesis:
[tex]\[
8 \times 4 + 8 \times n = 112
\][/tex]
[tex]\[
32 + 8n = 112
\][/tex]
- Subtract 32 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
8n = 112 - 32
\][/tex]
[tex]\[
8n = 80
\][/tex]
- Divide both sides by 8 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{80}{8}
\][/tex]
[tex]\[
n = 10
\][/tex]
So, the number we are looking for is [tex]\( n = 10 \)[/tex]. The correct equation that represents this scenario is [tex]\( 8(4 + n) = 112 \)[/tex].
We are given that the product of 8 and the sum of 4 and a number equals 112. We need to find what that number is.
1. Translate the words into an equation:
- The phrase "the sum of 4 and a number" suggests we add 4 to a number, which we can call [tex]\( n \)[/tex].
- So, 4 + [tex]\( n \)[/tex].
- The phrase "the product of 8 and" tells us we should multiply 8 by this sum.
- Therefore, we write it as: [tex]\( 8 \times (4 + n) \)[/tex].
2. Set up the equation:
- According to the problem, this product equals 112. Therefore, our equation is:
[tex]\[
8(4 + n) = 112
\][/tex]
3. Solve the equation for [tex]\( n \)[/tex]:
- Distribute the 8 to both terms inside the parenthesis:
[tex]\[
8 \times 4 + 8 \times n = 112
\][/tex]
[tex]\[
32 + 8n = 112
\][/tex]
- Subtract 32 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
8n = 112 - 32
\][/tex]
[tex]\[
8n = 80
\][/tex]
- Divide both sides by 8 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{80}{8}
\][/tex]
[tex]\[
n = 10
\][/tex]
So, the number we are looking for is [tex]\( n = 10 \)[/tex]. The correct equation that represents this scenario is [tex]\( 8(4 + n) = 112 \)[/tex].
