Answer :
To solve the problem, we need to set up and solve an equation based on the given information. Let's break it down step-by-step.
1. Understand the problem:
We have a number, [tex]\( n \)[/tex], and we add it to a value that is 15 less than 3 times itself. The sum of these expressions equals 101.
2. Translate the words into an equation:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is added to this expression, which gives us [tex]\( n + (3n - 15) \)[/tex].
- This sum equals 101.
3. Write the equation:
[tex]\[
n + 3n - 15 = 101
\][/tex]
4. Combine like terms:
Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex] to get:
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve the equation:
- Add 15 to both sides to isolate terms with [tex]\( n \)[/tex]:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4}
\][/tex]
6. Calculate the result:
[tex]\[
n = 29
\][/tex]
Therefore, the number [tex]\( n \)[/tex] is 29.
1. Understand the problem:
We have a number, [tex]\( n \)[/tex], and we add it to a value that is 15 less than 3 times itself. The sum of these expressions equals 101.
2. Translate the words into an equation:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is added to this expression, which gives us [tex]\( n + (3n - 15) \)[/tex].
- This sum equals 101.
3. Write the equation:
[tex]\[
n + 3n - 15 = 101
\][/tex]
4. Combine like terms:
Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex] to get:
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve the equation:
- Add 15 to both sides to isolate terms with [tex]\( n \)[/tex]:
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4}
\][/tex]
6. Calculate the result:
[tex]\[
n = 29
\][/tex]
Therefore, the number [tex]\( n \)[/tex] is 29.
