Answer :
To solve the problem, we need to determine which equation can be used to find the value of [tex]\( n \)[/tex] given that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself, resulting in 101.
Let's break it down step-by-step:
1. Understanding the Problem Statement:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], resulting in [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is then added to this expression: [tex]\( n + (3n - 15) \)[/tex].
2. Setting Up the Equation:
- According to the problem, adding these results in a total of 101. Therefore, our equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplifying the Equation:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex].
- The equation now simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
4. Rearranging and Solving:
- To isolate [tex]\( n \)[/tex], first add 15 to both sides:
[tex]\[
4n - 15 + 15 = 101 + 15 \\
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
Therefore, the correct equation to use is [tex]\( 3n - 15 + n = 101 \)[/tex], which simplifies to [tex]\( 4n - 15 = 101 \)[/tex]. Solving this equation gives us [tex]\( n = 29 \)[/tex]. Thus, the equation we were looking for from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
Let's break it down step-by-step:
1. Understanding the Problem Statement:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], resulting in [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is then added to this expression: [tex]\( n + (3n - 15) \)[/tex].
2. Setting Up the Equation:
- According to the problem, adding these results in a total of 101. Therefore, our equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplifying the Equation:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex].
- The equation now simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
4. Rearranging and Solving:
- To isolate [tex]\( n \)[/tex], first add 15 to both sides:
[tex]\[
4n - 15 + 15 = 101 + 15 \\
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
Therefore, the correct equation to use is [tex]\( 3n - 15 + n = 101 \)[/tex], which simplifies to [tex]\( 4n - 15 = 101 \)[/tex]. Solving this equation gives us [tex]\( n = 29 \)[/tex]. Thus, the equation we were looking for from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
