Answer :
To solve the problem and find the equation that can be used to determine the value of [tex]\( n \)[/tex], let's break it down step-by-step:
1. Understand the Problem:
- We have a number [tex]\( n \)[/tex].
- We are adding this number [tex]\( n \)[/tex] to "15 less than 3 times itself." This phrase can be translated mathematically as [tex]\( 3n - 15 \)[/tex].
2. Translate the Words to an Equation:
- "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself." This means we're forming the equation:
[tex]\[
n + (3n - 15)
\][/tex]
- The result of this addition is 101, so we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the Equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
- Therefore, the correct form of the equation to find [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
The equation [tex]\( 3n - 15 + n = 101 \)[/tex] can be used to find the value of [tex]\( n \)[/tex]. Solving this equation reveals that the value of [tex]\( n \)[/tex] is indeed 29.
So, the correct choice from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
1. Understand the Problem:
- We have a number [tex]\( n \)[/tex].
- We are adding this number [tex]\( n \)[/tex] to "15 less than 3 times itself." This phrase can be translated mathematically as [tex]\( 3n - 15 \)[/tex].
2. Translate the Words to an Equation:
- "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself." This means we're forming the equation:
[tex]\[
n + (3n - 15)
\][/tex]
- The result of this addition is 101, so we set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the Equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
- Therefore, the correct form of the equation to find [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
The equation [tex]\( 3n - 15 + n = 101 \)[/tex] can be used to find the value of [tex]\( n \)[/tex]. Solving this equation reveals that the value of [tex]\( n \)[/tex] is indeed 29.
So, the correct choice from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
