Answer :
To find the equation that can be used to find the value of [tex]\( n \)[/tex], let's break down the problem step-by-step:
1. Understand the problem statement:
- We have a number [tex]\( n \)[/tex].
- It is added to "15 less than 3 times itself."
2. Translate the words into a mathematical expression:
- "3 times itself" would mean [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means subtracting 15 from [tex]\( 3n \)[/tex], which gives us [tex]\( 3n - 15 \)[/tex].
3. Form the expression:
- The number [tex]\( n \)[/tex] is added to this value: [tex]\( n + (3n - 15) \)[/tex].
4. Set up the equation based on the problem:
- The result of this addition equals 101. So, we can write the equation as:
[tex]\[
n + (3n - 15) = 101
\][/tex]
5. Combine like terms:
- Combine the [tex]\( n \)[/tex] terms:
[tex]\[
1n + 3n - 15 = 101
\][/tex]
- This simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
6. Conclusion:
- The equation that represents the problem is [tex]\( 3n - 15 + n = 101 \)[/tex].
Therefore, the correct equation from the options given is [tex]\( 3n - 15 + n = 101 \)[/tex].
1. Understand the problem statement:
- We have a number [tex]\( n \)[/tex].
- It is added to "15 less than 3 times itself."
2. Translate the words into a mathematical expression:
- "3 times itself" would mean [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means subtracting 15 from [tex]\( 3n \)[/tex], which gives us [tex]\( 3n - 15 \)[/tex].
3. Form the expression:
- The number [tex]\( n \)[/tex] is added to this value: [tex]\( n + (3n - 15) \)[/tex].
4. Set up the equation based on the problem:
- The result of this addition equals 101. So, we can write the equation as:
[tex]\[
n + (3n - 15) = 101
\][/tex]
5. Combine like terms:
- Combine the [tex]\( n \)[/tex] terms:
[tex]\[
1n + 3n - 15 = 101
\][/tex]
- This simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
6. Conclusion:
- The equation that represents the problem is [tex]\( 3n - 15 + n = 101 \)[/tex].
Therefore, the correct equation from the options given is [tex]\( 3n - 15 + n = 101 \)[/tex].
