Answer :
To find the correct equation for this problem, let's break down the question step by step:
We are told that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself. The result of this operation is 101. Let's translate this information into a mathematical expression:
1. Three times the number [tex]\( n \)[/tex]: This can be written as [tex]\( 3n \)[/tex].
2. 15 less than three times the number: This means we subtract 15 from [tex]\( 3n \)[/tex], giving us [tex]\( 3n - 15 \)[/tex].
3. The number [tex]\( n \)[/tex] is added to the result of the above: This means we take [tex]\( 3n - 15 \)[/tex] and add [tex]\( n \)[/tex] to it. The expression becomes [tex]\( (3n - 15) + n \)[/tex].
4. The result is 101: So, we set the expression equal to 101. This gives us the equation:
[tex]\[
3n - 15 + n = 101
\][/tex]
Now, let's simplify the left side of the equation:
- Combine like terms: [tex]\( 3n + n = 4n \)[/tex]
Thus, the equation simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
This is the equation we can use to find the value of [tex]\( n \)[/tex]. By solving this equation, we find that [tex]\( n = 29 \)[/tex].
So, the correct equation, which can be used to find the value of [tex]\( n \)[/tex], is:
[tex]\[
3n - 15 + n = 101
\][/tex]
We are told that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself. The result of this operation is 101. Let's translate this information into a mathematical expression:
1. Three times the number [tex]\( n \)[/tex]: This can be written as [tex]\( 3n \)[/tex].
2. 15 less than three times the number: This means we subtract 15 from [tex]\( 3n \)[/tex], giving us [tex]\( 3n - 15 \)[/tex].
3. The number [tex]\( n \)[/tex] is added to the result of the above: This means we take [tex]\( 3n - 15 \)[/tex] and add [tex]\( n \)[/tex] to it. The expression becomes [tex]\( (3n - 15) + n \)[/tex].
4. The result is 101: So, we set the expression equal to 101. This gives us the equation:
[tex]\[
3n - 15 + n = 101
\][/tex]
Now, let's simplify the left side of the equation:
- Combine like terms: [tex]\( 3n + n = 4n \)[/tex]
Thus, the equation simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
This is the equation we can use to find the value of [tex]\( n \)[/tex]. By solving this equation, we find that [tex]\( n = 29 \)[/tex].
So, the correct equation, which can be used to find the value of [tex]\( n \)[/tex], is:
[tex]\[
3n - 15 + n = 101
\][/tex]
