Answer :
To solve this problem, we need to break down the words into mathematical expressions and create an equation. Let's do this step-by-step:
1. Understanding the Problem:
- We have a number, which we'll call [tex]\( n \)[/tex].
- This number is added to another expression: "15 less than 3 times itself."
2. Translating Words to Math:
- "3 times itself" can be written as [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], giving us [tex]\( 3n - 15 \)[/tex].
3. Setting Up the Equation:
- The problem states that when [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex], the result is 101. So we add [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex] and set the expression equal to 101:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplifying the Equation:
- Combine like terms: [tex]\( n + 3n \)[/tex] becomes [tex]\( 4n \)[/tex], so we have:
[tex]\[
4n - 15 = 101
\][/tex]
5. Solving the Equation:
- To isolate [tex]\( n \)[/tex], add 15 to both sides:
[tex]\[
4n = 116
\][/tex]
- Divide by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = 29
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And the solution process confirms that this is the correct setup for the problem.
1. Understanding the Problem:
- We have a number, which we'll call [tex]\( n \)[/tex].
- This number is added to another expression: "15 less than 3 times itself."
2. Translating Words to Math:
- "3 times itself" can be written as [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], giving us [tex]\( 3n - 15 \)[/tex].
3. Setting Up the Equation:
- The problem states that when [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex], the result is 101. So we add [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex] and set the expression equal to 101:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplifying the Equation:
- Combine like terms: [tex]\( n + 3n \)[/tex] becomes [tex]\( 4n \)[/tex], so we have:
[tex]\[
4n - 15 = 101
\][/tex]
5. Solving the Equation:
- To isolate [tex]\( n \)[/tex], add 15 to both sides:
[tex]\[
4n = 116
\][/tex]
- Divide by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = 29
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And the solution process confirms that this is the correct setup for the problem.
