Answer :
To solve the problem, let's break it down step by step:
1. Understanding the expression:
We need to express the statement in the problem as an equation. The statement says a number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. Let's represent this in algebraic terms:
- "3 times itself" is [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" is [tex]\( 3n - 15 \)[/tex].
2. Setting up the equation:
The problem says this result when added to [tex]\( n \)[/tex] equals 101. So, we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplifying the equation:
Now, let's simplify it:
- Combine the [tex]\( n \)[/tex] terms: [tex]\( n + 3n = 4n \)[/tex]
So the equation becomes:
[tex]\[
4n - 15 = 101
\][/tex]
4. Identifying the correct equation:
The equation we derived from the problem statement is the one where [tex]\( n \)[/tex] is added to 15 less than 3 times itself, which simplifies to:
[tex]\[
3n - 15 + n = 101
\][/tex]
Therefore, the correct choice among the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
The chosen equation reflects the logic described in the problem.
1. Understanding the expression:
We need to express the statement in the problem as an equation. The statement says a number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. Let's represent this in algebraic terms:
- "3 times itself" is [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" is [tex]\( 3n - 15 \)[/tex].
2. Setting up the equation:
The problem says this result when added to [tex]\( n \)[/tex] equals 101. So, we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplifying the equation:
Now, let's simplify it:
- Combine the [tex]\( n \)[/tex] terms: [tex]\( n + 3n = 4n \)[/tex]
So the equation becomes:
[tex]\[
4n - 15 = 101
\][/tex]
4. Identifying the correct equation:
The equation we derived from the problem statement is the one where [tex]\( n \)[/tex] is added to 15 less than 3 times itself, which simplifies to:
[tex]\[
3n - 15 + n = 101
\][/tex]
Therefore, the correct choice among the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
The chosen equation reflects the logic described in the problem.
