Answer :
Let's solve the problem step-by-step.
We start with the information given: A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself, and the result is 101. We need to translate this into an equation.
1. Translate the problem into words:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- "A number, [tex]\( n \)[/tex], is added..." means we add the number [tex]\( n \)[/tex] that we are trying to find.
- The entire expression becomes: [tex]\( n + (3n - 15) \)[/tex].
2. Form the equation:
- Combining everything, the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
- Simplifying inside the parentheses, we have:
[tex]\[
3n - 15
\][/tex]
- So, the equation now looks like:
[tex]\[
n + 3n - 15 = 101
\][/tex]
3. Combine like terms:
- Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex]:
[tex]\[
4n - 15 = 101
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n = 101 + 15
\][/tex]
- Simplify the right side:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4}
\][/tex]
- Calculate the division:
[tex]\[
n = 29
\][/tex]
Therefore, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is [tex]\( 3n - 15 + n = 101 \)[/tex], and the value of [tex]\( n \)[/tex] is 29.
We start with the information given: A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself, and the result is 101. We need to translate this into an equation.
1. Translate the problem into words:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- "A number, [tex]\( n \)[/tex], is added..." means we add the number [tex]\( n \)[/tex] that we are trying to find.
- The entire expression becomes: [tex]\( n + (3n - 15) \)[/tex].
2. Form the equation:
- Combining everything, the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
- Simplifying inside the parentheses, we have:
[tex]\[
3n - 15
\][/tex]
- So, the equation now looks like:
[tex]\[
n + 3n - 15 = 101
\][/tex]
3. Combine like terms:
- Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex]:
[tex]\[
4n - 15 = 101
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n = 101 + 15
\][/tex]
- Simplify the right side:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4}
\][/tex]
- Calculate the division:
[tex]\[
n = 29
\][/tex]
Therefore, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is [tex]\( 3n - 15 + n = 101 \)[/tex], and the value of [tex]\( n \)[/tex] is 29.
