Answer :
To find the correct equation that can be used to determine the value of [tex]\( n \)[/tex], follow these steps:
1. Translate the problem into an equation:
- We are given that a number [tex]\( n \)[/tex] is added to "15 less than 3 times itself."
- The expression "3 times itself" is [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], giving us [tex]\( 3n - 15 \)[/tex].
- We add [tex]\( n \)[/tex] to this expression to get the result: [tex]\( n + (3n - 15) = 101 \)[/tex].
2. Combine like terms:
- Combine the terms involving [tex]\( n \)[/tex] in the equation [tex]\( n + 3n - 15 = 101 \)[/tex].
- This simplifies to [tex]\( 4n - 15 = 101 \)[/tex].
3. Formulate the equation:
- Rearranging the equation gives: [tex]\( 3n - 15 + n = 101 \)[/tex].
Therefore, the correct equation to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This equation matches the first option provided:
[tex]\[ 3n - 15 + n = 101 \][/tex]
Now, let's solve the equation for [tex]\( n \)[/tex]:
1. Simplify the equation:
- Combine the [tex]\( n \)[/tex] terms: [tex]\( 4n - 15 = 101 \)[/tex].
2. Add 15 to both sides:
- [tex]\( 4n - 15 + 15 = 101 + 15 \)[/tex]
- This results in: [tex]\( 4n = 116 \)[/tex].
3. Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
- [tex]\( \frac{4n}{4} = \frac{116}{4} \)[/tex]
- This simplifies to: [tex]\( n = 29 \)[/tex].
Hence, the value of [tex]\( n \)[/tex] is 29.
1. Translate the problem into an equation:
- We are given that a number [tex]\( n \)[/tex] is added to "15 less than 3 times itself."
- The expression "3 times itself" is [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means we subtract 15 from [tex]\( 3n \)[/tex], giving us [tex]\( 3n - 15 \)[/tex].
- We add [tex]\( n \)[/tex] to this expression to get the result: [tex]\( n + (3n - 15) = 101 \)[/tex].
2. Combine like terms:
- Combine the terms involving [tex]\( n \)[/tex] in the equation [tex]\( n + 3n - 15 = 101 \)[/tex].
- This simplifies to [tex]\( 4n - 15 = 101 \)[/tex].
3. Formulate the equation:
- Rearranging the equation gives: [tex]\( 3n - 15 + n = 101 \)[/tex].
Therefore, the correct equation to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This equation matches the first option provided:
[tex]\[ 3n - 15 + n = 101 \][/tex]
Now, let's solve the equation for [tex]\( n \)[/tex]:
1. Simplify the equation:
- Combine the [tex]\( n \)[/tex] terms: [tex]\( 4n - 15 = 101 \)[/tex].
2. Add 15 to both sides:
- [tex]\( 4n - 15 + 15 = 101 + 15 \)[/tex]
- This results in: [tex]\( 4n = 116 \)[/tex].
3. Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
- [tex]\( \frac{4n}{4} = \frac{116}{4} \)[/tex]
- This simplifies to: [tex]\( n = 29 \)[/tex].
Hence, the value of [tex]\( n \)[/tex] is 29.
