Answer :
To solve the problem, we need to translate the given situation into a mathematical equation. Let's go through the steps:
1. Understanding the Problem:
- We have a number, [tex]\( n \)[/tex].
- We are adding this number, [tex]\( n \)[/tex], to a certain expression.
- The expression is "15 less than 3 times the number", which means we take 3 times the number, [tex]\( 3n \)[/tex], and subtract 15 from it.
2. Setting Up the Expression:
- The expression "15 less than 3 times the number" can be written as [tex]\( 3n - 15 \)[/tex].
3. Adding the Number to the Expression:
- We are adding the number [tex]\( n \)[/tex] to the expression [tex]\( 3n - 15 \)[/tex]. So, it becomes [tex]\( n + (3n - 15) \)[/tex].
4. Writing the Equation:
- The problem states that the result of the addition is 101. Therefore, the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
5. Simplifying the Equation:
- Combine the terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
- Simplify the left side by combining like terms ([tex]\(n + 3n\)[/tex] becomes [tex]\(4n\)[/tex]):
[tex]\[
4n - 15 = 101
\][/tex]
6. Choosing the Correct Option:
- From the options provided, the equation that matches our derived equation is:
[tex]\(3n - 15 + n = 101\)[/tex]
This option, when simplified, correctly provides the equation [tex]\(4n - 15 = 101\)[/tex], which is used to find the value of [tex]\( n \)[/tex].
1. Understanding the Problem:
- We have a number, [tex]\( n \)[/tex].
- We are adding this number, [tex]\( n \)[/tex], to a certain expression.
- The expression is "15 less than 3 times the number", which means we take 3 times the number, [tex]\( 3n \)[/tex], and subtract 15 from it.
2. Setting Up the Expression:
- The expression "15 less than 3 times the number" can be written as [tex]\( 3n - 15 \)[/tex].
3. Adding the Number to the Expression:
- We are adding the number [tex]\( n \)[/tex] to the expression [tex]\( 3n - 15 \)[/tex]. So, it becomes [tex]\( n + (3n - 15) \)[/tex].
4. Writing the Equation:
- The problem states that the result of the addition is 101. Therefore, the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
5. Simplifying the Equation:
- Combine the terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
- Simplify the left side by combining like terms ([tex]\(n + 3n\)[/tex] becomes [tex]\(4n\)[/tex]):
[tex]\[
4n - 15 = 101
\][/tex]
6. Choosing the Correct Option:
- From the options provided, the equation that matches our derived equation is:
[tex]\(3n - 15 + n = 101\)[/tex]
This option, when simplified, correctly provides the equation [tex]\(4n - 15 = 101\)[/tex], which is used to find the value of [tex]\( n \)[/tex].
