Answer :
Sure! Let's solve the problem step-by-step.
Given:
- A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself.
- The result is 101.
We need to find the equation that helps to determine the value of [tex]\( n \)[/tex].
### Step-by-Step Solution
1. Understanding the Problem:
- We have a number [tex]\( n \)[/tex].
- We need to add this number [tex]\( n \)[/tex] to another expression which is:
[tex]\[
15 \text{ less than 3 times } n
\][/tex]
- The sum is equal to 101.
2. Forming the Expression:
- "3 times [tex]\( n \)[/tex]" can be written as:
[tex]\[
3n
\][/tex]
- "15 less than 3 times [tex]\( n \)[/tex]" means we subtract 15 from [tex]\( 3n \)[/tex]:
[tex]\[
3n - 15
\][/tex]
- Now, we add [tex]\( n \)[/tex] to this expression:
[tex]\[
n + (3n - 15)
\][/tex]
3. Writing the Equation:
- According to the problem, the above sum is equal to 101. So we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplifying the Equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
5. Solving for [tex]\( n \)[/tex]:
- Add 15 to both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Now, divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
6. Conclusion:
- Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
The correct equation from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the equation is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And the value of [tex]\( n \)[/tex] is:
[tex]\[
n = 29
\][/tex]
Given:
- A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself.
- The result is 101.
We need to find the equation that helps to determine the value of [tex]\( n \)[/tex].
### Step-by-Step Solution
1. Understanding the Problem:
- We have a number [tex]\( n \)[/tex].
- We need to add this number [tex]\( n \)[/tex] to another expression which is:
[tex]\[
15 \text{ less than 3 times } n
\][/tex]
- The sum is equal to 101.
2. Forming the Expression:
- "3 times [tex]\( n \)[/tex]" can be written as:
[tex]\[
3n
\][/tex]
- "15 less than 3 times [tex]\( n \)[/tex]" means we subtract 15 from [tex]\( 3n \)[/tex]:
[tex]\[
3n - 15
\][/tex]
- Now, we add [tex]\( n \)[/tex] to this expression:
[tex]\[
n + (3n - 15)
\][/tex]
3. Writing the Equation:
- According to the problem, the above sum is equal to 101. So we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplifying the Equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
5. Solving for [tex]\( n \)[/tex]:
- Add 15 to both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Now, divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
6. Conclusion:
- Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
The correct equation from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
So, the equation is:
[tex]\[
3n - 15 + n = 101
\][/tex]
And the value of [tex]\( n \)[/tex] is:
[tex]\[
n = 29
\][/tex]
