College

A number, [tex]n[/tex], is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of [tex]n[/tex]?

A. [tex]3n - 15 + n = 101[/tex]
B. [tex]3n + 15 + n = 101[/tex]
C. [tex]3n - 15 - n = 101[/tex]
D. [tex]3n + 15 - n = 101[/tex]

Answer :

Sure! Let's solve the problem step-by-step to find out which equation can be used to determine the value of [tex]\( n \)[/tex].

1. Understand the problem statement:
- We are given that a number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself.
- This sum equals 101.

2. Translate the problem into an equation:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" translates to [tex]\( 3n - 15 \)[/tex].
- Adding [tex]\( n \)[/tex] to this expression gives us: [tex]\( n + (3n - 15) \)[/tex].

3. Set up the equation:
- The equation based on the problem statement is:
[tex]\[
n + (3n - 15) = 101
\][/tex]

4. Simplify the equation:
- Combine like terms:
[tex]\[
n + 3n = 4n
\][/tex]
- So, the equation becomes:
[tex]\[
4n - 15 = 101
\][/tex]

Based on the steps above, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:

[tex]\[
3n - 15 + n = 101
\][/tex]

This corresponds to the first option in the list provided:

[tex]\[
3n - 15 + n = 101
\][/tex]

This setup aligns with creating an accurate equation from the problem description.

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