Answer :
To solve the problem, let's translate the given information into a mathematical equation and solve it step-by-step.
1. Translation of the problem into an equation:
- We are given a number, [tex]\( n \)[/tex].
- We need to add this number to 15 less than 3 times itself.
- The result of this addition is given as 101.
2. Forming the equation:
- Firstly, 3 times the number [tex]\( n \)[/tex] is [tex]\( 3n \)[/tex].
- 15 less than 3 times the number is [tex]\( 3n - 15 \)[/tex].
- Adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex] gives us [tex]\( n + (3n - 15) \)[/tex].
- This sum equals 101.
Therefore, the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplifying the equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
- Simplifying the left side, we get:
[tex]\[
4n - 15 = 101
\][/tex]
4. Solving for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
Simplifying this, we get:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
Solving this, we find:
[tex]\[
n = 29
\][/tex]
5. Conclusion:
- The correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the correct option from the given choices is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
1. Translation of the problem into an equation:
- We are given a number, [tex]\( n \)[/tex].
- We need to add this number to 15 less than 3 times itself.
- The result of this addition is given as 101.
2. Forming the equation:
- Firstly, 3 times the number [tex]\( n \)[/tex] is [tex]\( 3n \)[/tex].
- 15 less than 3 times the number is [tex]\( 3n - 15 \)[/tex].
- Adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex] gives us [tex]\( n + (3n - 15) \)[/tex].
- This sum equals 101.
Therefore, the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplifying the equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
- Simplifying the left side, we get:
[tex]\[
4n - 15 = 101
\][/tex]
4. Solving for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
Simplifying this, we get:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
Solving this, we find:
[tex]\[
n = 29
\][/tex]
5. Conclusion:
- The correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the correct option from the given choices is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
