Answer :
To solve the problem, let's break down the statement:
The problem states that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself, and the result is 101. We need to find which equation correctly represents this situation.
1. Understand "3 times itself":
- Three times the number [tex]\( n \)[/tex] would be [tex]\( 3n \)[/tex].
2. Understand "15 less than 3 times itself":
- This means we take 3 times the number [tex]\( n \)[/tex] and subtract 15, making it [tex]\( 3n - 15 \)[/tex].
3. Setting up the equation:
- According to the problem, the number [tex]\( n \)[/tex] is added to "15 less than 3 times itself." This would be the number [tex]\( n \)[/tex] plus [tex]\( 3n - 15 \)[/tex].
- Therefore, the full expression is [tex]\( n + (3n - 15) \)[/tex].
4. Writing the equation:
- Simplify the expression: [tex]\( n + 3n - 15 \)[/tex] becomes [tex]\( 4n - 15 \)[/tex].
- This result is set equal to 101 according to the problem condition.
- So the equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
The correct equation from the given options is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This aligns with our understanding and simplification of the problem statement.
The problem states that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself, and the result is 101. We need to find which equation correctly represents this situation.
1. Understand "3 times itself":
- Three times the number [tex]\( n \)[/tex] would be [tex]\( 3n \)[/tex].
2. Understand "15 less than 3 times itself":
- This means we take 3 times the number [tex]\( n \)[/tex] and subtract 15, making it [tex]\( 3n - 15 \)[/tex].
3. Setting up the equation:
- According to the problem, the number [tex]\( n \)[/tex] is added to "15 less than 3 times itself." This would be the number [tex]\( n \)[/tex] plus [tex]\( 3n - 15 \)[/tex].
- Therefore, the full expression is [tex]\( n + (3n - 15) \)[/tex].
4. Writing the equation:
- Simplify the expression: [tex]\( n + 3n - 15 \)[/tex] becomes [tex]\( 4n - 15 \)[/tex].
- This result is set equal to 101 according to the problem condition.
- So the equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
The correct equation from the given options is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This aligns with our understanding and simplification of the problem statement.
