Answer :
To solve the problem, let's first understand what is being asked:
We need to form an equation based on the statement "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. The result is 101."
1. Express the situation in mathematical terms:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- If [tex]\( n \)[/tex] is added to this amount, the expression becomes [tex]\( n + (3n - 15) \)[/tex].
2. Set up the equation:
We know that the result of the above expression is 101. So the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
Which simplifies to:
[tex]\[
3n - 15 + n = 101
\][/tex]
3. Combine like terms:
- Combine the [tex]\( n \)[/tex] terms:
[tex]\[
3n + n = 4n
\][/tex]
This gives us:
[tex]\[
4n - 15 = 101
\][/tex]
Therefore, the equation [tex]\( 3n - 15 + n = 101 \)[/tex] can be used to find the value of [tex]\( n \)[/tex]. This matches the first choice in your options.
We need to form an equation based on the statement "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. The result is 101."
1. Express the situation in mathematical terms:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- If [tex]\( n \)[/tex] is added to this amount, the expression becomes [tex]\( n + (3n - 15) \)[/tex].
2. Set up the equation:
We know that the result of the above expression is 101. So the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
Which simplifies to:
[tex]\[
3n - 15 + n = 101
\][/tex]
3. Combine like terms:
- Combine the [tex]\( n \)[/tex] terms:
[tex]\[
3n + n = 4n
\][/tex]
This gives us:
[tex]\[
4n - 15 = 101
\][/tex]
Therefore, the equation [tex]\( 3n - 15 + n = 101 \)[/tex] can be used to find the value of [tex]\( n \)[/tex]. This matches the first choice in your options.
