Answer :
Sure! Let's solve the problem step-by-step.
The problem states: A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. The result is 101. We need to form an equation based on this information.
1. Understand and translate the words into an equation:
- "Three times itself": This means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself": This means [tex]\( 3n - 15 \)[/tex].
- "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself": This means [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex].
2. Form the equation:
When [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex], the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the equation:
Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
This simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
Therefore, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
This corresponds to the first option in the list provided:
[tex]\[
3n - 15 + n = 101
\][/tex]
The problem states: A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. The result is 101. We need to form an equation based on this information.
1. Understand and translate the words into an equation:
- "Three times itself": This means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself": This means [tex]\( 3n - 15 \)[/tex].
- "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself": This means [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex].
2. Form the equation:
When [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex], the equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the equation:
Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
This simplifies to:
[tex]\[
4n - 15 = 101
\][/tex]
Therefore, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
This corresponds to the first option in the list provided:
[tex]\[
3n - 15 + n = 101
\][/tex]
