Answer :
Sure! Let's solve the problem step-by-step.
### Problem Statement
A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself. The result is 101. We need to find which equation can be used to determine the value of [tex]\( n \)[/tex].
### Step-by-Step Solution
1. Understand the Problem:
- We are given a number [tex]\( n \)[/tex].
- We need to add [tex]\( n \)[/tex] to a value which is 15 less than 3 times [tex]\( n \)[/tex].
- The equation then needs to equal 101.
2. Translate the Statement into an Equation:
- "A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself":
- Three times [tex]\( n \)[/tex] is written as [tex]\( 3n \)[/tex].
- 15 less than 3 times [tex]\( n \)[/tex] is written as [tex]\( 3n - 15 \)[/tex].
- Adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex]:
[tex]\[
n + (3n - 15)
\][/tex]
3. Formulate the Equation:
- The resultant value is given as 101:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplify the Equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4:
[tex]\[
n = 116 / 4
\][/tex]
[tex]\[
n = 29
\][/tex]
### Conclusion
The equation that represents the given problem is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And the value of [tex]\( n \)[/tex] is:
[tex]\[
n = 29
\][/tex]
So, the correct equation that can be used to find [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
This corresponds to the first option in the given choices:
[tex]\[
\boxed{3n - 15 + n = 101}
\][/tex]
### Problem Statement
A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself. The result is 101. We need to find which equation can be used to determine the value of [tex]\( n \)[/tex].
### Step-by-Step Solution
1. Understand the Problem:
- We are given a number [tex]\( n \)[/tex].
- We need to add [tex]\( n \)[/tex] to a value which is 15 less than 3 times [tex]\( n \)[/tex].
- The equation then needs to equal 101.
2. Translate the Statement into an Equation:
- "A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself":
- Three times [tex]\( n \)[/tex] is written as [tex]\( 3n \)[/tex].
- 15 less than 3 times [tex]\( n \)[/tex] is written as [tex]\( 3n - 15 \)[/tex].
- Adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex]:
[tex]\[
n + (3n - 15)
\][/tex]
3. Formulate the Equation:
- The resultant value is given as 101:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplify the Equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4:
[tex]\[
n = 116 / 4
\][/tex]
[tex]\[
n = 29
\][/tex]
### Conclusion
The equation that represents the given problem is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And the value of [tex]\( n \)[/tex] is:
[tex]\[
n = 29
\][/tex]
So, the correct equation that can be used to find [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
This corresponds to the first option in the given choices:
[tex]\[
\boxed{3n - 15 + n = 101}
\][/tex]
