Answer :
Sure! Let's work through the problem step by step.
The problem states:
- A number [tex]\( n \)[/tex] is added to [tex]\( 15 \)[/tex] less than [tex]\( 3 \)[/tex] times itself.
- The result is [tex]\( 101 \)[/tex].
First, we need to translate this statement into a mathematical equation.
1. Identify the expressions:
- "3 times itself": This is [tex]\( 3n \)[/tex].
- "15 less than 3 times itself": This is [tex]\( 3n - 15 \)[/tex].
2. Form the equation:
- The number [tex]\( n \)[/tex] is added to [tex]\( 15 \)[/tex] less than [tex]\( 3 \)[/tex] times itself, which means [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex].
- So, we write this as [tex]\( n + (3n - 15) \)[/tex].
3. Set up the equation for the given result:
- The result of the addition is [tex]\( 101 \)[/tex], so we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Combine like terms:
- Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex]:
[tex]\[
n + 3n - 15 = 101
\][/tex]
- This simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
From this process, we see that the correct equation to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{3n - 15 + n = 101}
\][/tex]
The problem states:
- A number [tex]\( n \)[/tex] is added to [tex]\( 15 \)[/tex] less than [tex]\( 3 \)[/tex] times itself.
- The result is [tex]\( 101 \)[/tex].
First, we need to translate this statement into a mathematical equation.
1. Identify the expressions:
- "3 times itself": This is [tex]\( 3n \)[/tex].
- "15 less than 3 times itself": This is [tex]\( 3n - 15 \)[/tex].
2. Form the equation:
- The number [tex]\( n \)[/tex] is added to [tex]\( 15 \)[/tex] less than [tex]\( 3 \)[/tex] times itself, which means [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex].
- So, we write this as [tex]\( n + (3n - 15) \)[/tex].
3. Set up the equation for the given result:
- The result of the addition is [tex]\( 101 \)[/tex], so we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Combine like terms:
- Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex]:
[tex]\[
n + 3n - 15 = 101
\][/tex]
- This simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
From this process, we see that the correct equation to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{3n - 15 + n = 101}
\][/tex]
