Answer :
To solve this problem, we need to create an equation based on the description provided. Let's break it down step-by-step:
1. We are given that a number [tex]\( n \)[/tex] is added to "15 less than 3 times itself."
- "3 times itself" refers to [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], which gives us [tex]\( 3n - 15 \)[/tex].
2. The problem states that when you add [tex]\( n \)[/tex] to this expression ([tex]\( 3n - 15 \)[/tex]), the result is 101. So we can write the equation as:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the equation:
- First, combine like terms: [tex]\( n + 3n = 4n \)[/tex].
- So, the equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
4. To solve for [tex]\( n \)[/tex], first add 15 to both sides of the equation to get rid of the [tex]\(-15\)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
5. Next, divide both sides by 4 to isolate [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
Therefore, the correct equation from the given options that leads us to the solution is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And by solving this equation, we find that the value of [tex]\( n \)[/tex] is 29.
1. We are given that a number [tex]\( n \)[/tex] is added to "15 less than 3 times itself."
- "3 times itself" refers to [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], which gives us [tex]\( 3n - 15 \)[/tex].
2. The problem states that when you add [tex]\( n \)[/tex] to this expression ([tex]\( 3n - 15 \)[/tex]), the result is 101. So we can write the equation as:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the equation:
- First, combine like terms: [tex]\( n + 3n = 4n \)[/tex].
- So, the equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
4. To solve for [tex]\( n \)[/tex], first add 15 to both sides of the equation to get rid of the [tex]\(-15\)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
5. Next, divide both sides by 4 to isolate [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
Therefore, the correct equation from the given options that leads us to the solution is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And by solving this equation, we find that the value of [tex]\( n \)[/tex] is 29.
