To solve the problem, let's break it down step by step.
1. Understanding the Problem:
- We have a number [tex]\( n \)[/tex].
- "3 times itself" refers to [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" translates to [tex]\( 3n - 15 \)[/tex].
- Adding the number [tex]\( n \)[/tex] and [tex]\( 15 \)[/tex] less than 3 times itself gives [tex]\( n + (3n - 15) \)[/tex].
- According to the problem, this sum is equal to 101.
2. Formulating the Equation:
- Now, we can write the equation based on the given information:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplifying the Equation:
- Combine like terms on the left-hand side of the equation:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
4. Solving the Equation:
- First, add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Then, divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
\frac{4n}{4} = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
5. Matching the Equation:
- The simplified form of the equation [tex]\( n + (3n - 15) = 101 \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
- Thus, the correct equation that matches the problem statement is:
[tex]\[
3n - 15 + n = 101
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
