Answer :
To solve this problem, we need to create an equation based on the given situation: A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself. The result is 101.
Let's break it down:
1. Start with the expression "3 times itself":
- When you see "3 times itself," for number [tex]\( n \)[/tex], you can write it as [tex]\( 3n \)[/tex].
2. Next, find "15 less than 3 times itself":
- "15 less than" means subtracting 15 from this expression. So, it becomes [tex]\( 3n - 15 \)[/tex].
3. According to the problem, this expression is added to the original number [tex]\( n \)[/tex]:
- Therefore, you're adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex].
4. The complete expression becomes:
[tex]\[
3n - 15 + n
\][/tex]
5. The problem states that the result of this is 101:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This equation matches the first option given: [tex]\( 3n - 15 + n = 101 \)[/tex].
Let's break it down:
1. Start with the expression "3 times itself":
- When you see "3 times itself," for number [tex]\( n \)[/tex], you can write it as [tex]\( 3n \)[/tex].
2. Next, find "15 less than 3 times itself":
- "15 less than" means subtracting 15 from this expression. So, it becomes [tex]\( 3n - 15 \)[/tex].
3. According to the problem, this expression is added to the original number [tex]\( n \)[/tex]:
- Therefore, you're adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex].
4. The complete expression becomes:
[tex]\[
3n - 15 + n
\][/tex]
5. The problem states that the result of this is 101:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This equation matches the first option given: [tex]\( 3n - 15 + n = 101 \)[/tex].
