Answer :
To solve the problem, let's break it down step-by-step. We are given that a number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself, and the result is 101. We need to find the correct equation to express this situation.
1. Understand the Problem:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- So, we are adding [tex]\( n \)[/tex] to [tex]\( (3n - 15) \)[/tex].
2. Form the Equation:
- Add the expressions: [tex]\( n + (3n - 15) \)[/tex].
- This simplifies to [tex]\( n + 3n - 15 \)[/tex].
3. Combine Like Terms:
- Combining like terms gives: [tex]\( 4n - 15 \)[/tex].
4. Set the Equation Equal to the Result:
- According to the problem, this result is 101.
- So, the equation is: [tex]\( 4n - 15 = 101 \)[/tex].
Now, let's compare this with the given options:
- [tex]\( 3n - 15 + n = 101 \)[/tex] simplifies to [tex]\( 4n - 15 = 101 \)[/tex].
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This is the correct equation that represents the situation described in the problem.
1. Understand the Problem:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- So, we are adding [tex]\( n \)[/tex] to [tex]\( (3n - 15) \)[/tex].
2. Form the Equation:
- Add the expressions: [tex]\( n + (3n - 15) \)[/tex].
- This simplifies to [tex]\( n + 3n - 15 \)[/tex].
3. Combine Like Terms:
- Combining like terms gives: [tex]\( 4n - 15 \)[/tex].
4. Set the Equation Equal to the Result:
- According to the problem, this result is 101.
- So, the equation is: [tex]\( 4n - 15 = 101 \)[/tex].
Now, let's compare this with the given options:
- [tex]\( 3n - 15 + n = 101 \)[/tex] simplifies to [tex]\( 4n - 15 = 101 \)[/tex].
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This is the correct equation that represents the situation described in the problem.
