Answer :
To solve this problem, we need to carefully translate the given verbal expression into a mathematical equation.
1. Start by understanding the expression:
- "A number, [tex]$n$[/tex], is added to 15 less than 3 times itself."
2. Break it down:
- "3 times itself" means [tex]\(3n\)[/tex].
- "15 less than 3 times itself" means you subtract 15 from [tex]\(3n\)[/tex]: [tex]\(3n - 15\)[/tex].
3. Combine with the start of the expression:
- "A number, [tex]$n$[/tex], is added to" means you take [tex]$n$[/tex] and add it to the previous expression: [tex]\(n + (3n - 15)\)[/tex].
4. The problem states this sum "is 101":
- This gives us the equation: [tex]\(n + (3n - 15) = 101\)[/tex].
5. Simplify the equation:
- Combine like terms: [tex]\(4n - 15 = 101\)[/tex].
6. Solve for [tex]$n$[/tex]:
- Add 15 to both sides: [tex]\(4n = 116\)[/tex].
- Divide by 4: [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].
Through this reasoning, we determined that the correct equation from the listed options is [tex]\(3n - 15 + n = 101\)[/tex], and the solution for [tex]\(n\)[/tex] is 29.
1. Start by understanding the expression:
- "A number, [tex]$n$[/tex], is added to 15 less than 3 times itself."
2. Break it down:
- "3 times itself" means [tex]\(3n\)[/tex].
- "15 less than 3 times itself" means you subtract 15 from [tex]\(3n\)[/tex]: [tex]\(3n - 15\)[/tex].
3. Combine with the start of the expression:
- "A number, [tex]$n$[/tex], is added to" means you take [tex]$n$[/tex] and add it to the previous expression: [tex]\(n + (3n - 15)\)[/tex].
4. The problem states this sum "is 101":
- This gives us the equation: [tex]\(n + (3n - 15) = 101\)[/tex].
5. Simplify the equation:
- Combine like terms: [tex]\(4n - 15 = 101\)[/tex].
6. Solve for [tex]$n$[/tex]:
- Add 15 to both sides: [tex]\(4n = 116\)[/tex].
- Divide by 4: [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].
Through this reasoning, we determined that the correct equation from the listed options is [tex]\(3n - 15 + n = 101\)[/tex], and the solution for [tex]\(n\)[/tex] is 29.
