Answer :
To solve this problem, let's break down the information given in the question:
1. We have a number, [tex]\( n \)[/tex].
2. This number is added to "15 less than 3 times itself". Mathematically, this can be represented as:
[tex]\[
3n - 15
\][/tex]
3. The total result of this addition is 101.
Now, we can write the expression for the given situation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
Simplifying the expression:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex]
- So the equation becomes:
[tex]\[
4n - 15 = 101
\][/tex]
Now, let's solve the equation [tex]\( 4n - 15 = 101 \)[/tex]:
1. Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
This simplifies to:
[tex]\[
4n = 116
\][/tex]
2. Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
To determine which equation can be used to find the value of [tex]\( n \)[/tex], look at the initial expression:
The equation that matches what we initially set up is:
[tex]\[
3n - 15 + n = 101
\][/tex]
Based on the options given, the correct one would be:
[tex]\[
3n - 15 + n = 101
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\( 3n - 15 + n = 101 \)[/tex]
1. We have a number, [tex]\( n \)[/tex].
2. This number is added to "15 less than 3 times itself". Mathematically, this can be represented as:
[tex]\[
3n - 15
\][/tex]
3. The total result of this addition is 101.
Now, we can write the expression for the given situation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
Simplifying the expression:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex]
- So the equation becomes:
[tex]\[
4n - 15 = 101
\][/tex]
Now, let's solve the equation [tex]\( 4n - 15 = 101 \)[/tex]:
1. Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
This simplifies to:
[tex]\[
4n = 116
\][/tex]
2. Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
To determine which equation can be used to find the value of [tex]\( n \)[/tex], look at the initial expression:
The equation that matches what we initially set up is:
[tex]\[
3n - 15 + n = 101
\][/tex]
Based on the options given, the correct one would be:
[tex]\[
3n - 15 + n = 101
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\( 3n - 15 + n = 101 \)[/tex]
