To find the number [tex]\( n \)[/tex] that satisfies the given condition, let's carefully break down and follow the steps described in the problem:
1. Restate the Problem: We're given that a number [tex]\( n \)[/tex] is added to "15 less than 3 times itself," and the result is 101.
2. Translate the Verbal Description into an Equation:
- "3 times itself" can be written as [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" can be written as [tex]\( 3n - 15 \)[/tex].
- Adding the number [tex]\( n \)[/tex] to this expression results in [tex]\( n + (3n - 15) \)[/tex].
3. Formulate the Equation:
- Based on the problem, this sum equals 101. Therefore, the correct equation is:
[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. Check for the Equation in the Choices Given:
- We compare the simplified form with the provided options.
- The equation [tex]\( 4n - 15 = 101 \)[/tex] can be traced back to its original unsimplified form:
[tex]\[
3n - 15 + n = 101
\][/tex]
Therefore, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
Among the choices provided:
- [tex]\( 3n - 15 + n = 101 \)[/tex]
- [tex]\( 3n + 15 + n = 101 \)[/tex]
- [tex]\( 3n - 15 - n = 101 \)[/tex]
- [tex]\( 3n + 15 - n = 101 \)[/tex]
The correct choice is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
Hence, the answer is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
