Answer :
To solve the problem "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. The result is 101," we need to create an equation based on this statement.
1. Identify the parts of the statement:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
2. Write the expression for what is being added:
- When you add the number [tex]\( n \)[/tex] to "15 less than 3 times itself," you get [tex]\( n + (3n - 15) \)[/tex].
3. Set up the equation with the result given in the problem:
- The whole expression equals 101, so:
[tex]\[ n + (3n - 15) = 101 \][/tex]
4. Simplify the equation:
- Combine like terms:
[tex]\[ n + 3n - 15 = 101 \][/tex]
[tex]\[ 4n - 15 = 101 \][/tex]
5. Write the equation:
- [tex]\( 4n - 15 = 101 \)[/tex] matches the structure of one of the given options.
So the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This matches the first option in the list:
- [tex]\( 3n - 15 + n = 101 \)[/tex]
1. Identify the parts of the statement:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
2. Write the expression for what is being added:
- When you add the number [tex]\( n \)[/tex] to "15 less than 3 times itself," you get [tex]\( n + (3n - 15) \)[/tex].
3. Set up the equation with the result given in the problem:
- The whole expression equals 101, so:
[tex]\[ n + (3n - 15) = 101 \][/tex]
4. Simplify the equation:
- Combine like terms:
[tex]\[ n + 3n - 15 = 101 \][/tex]
[tex]\[ 4n - 15 = 101 \][/tex]
5. Write the equation:
- [tex]\( 4n - 15 = 101 \)[/tex] matches the structure of one of the given options.
So the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This matches the first option in the list:
- [tex]\( 3n - 15 + n = 101 \)[/tex]
