Answer :
Sure! Let's solve the problem step by step.
We need to find a number [tex]\( n \)[/tex] such that when it is added to 15 less than three times itself, the result is 101.
1. Translate the words into an equation:
- "Three times itself" means [tex]\( 3n \)[/tex].
- "15 less than three times itself" means [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is added to this expression, so we have: [tex]\( n + (3n - 15) \)[/tex].
- The result is 101, so the equation becomes:
[tex]\[ n + (3n - 15) = 101 \][/tex]
2. Simplify the equation:
- Combine like terms: [tex]\( n + 3n \)[/tex] becomes [tex]\( 4n \)[/tex].
- So the equation simplifies to:
[tex]\[ 4n - 15 = 101 \][/tex]
3. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
The correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
And solving this equation as shown above, we find that [tex]\( n \)[/tex] is 29.
We need to find a number [tex]\( n \)[/tex] such that when it is added to 15 less than three times itself, the result is 101.
1. Translate the words into an equation:
- "Three times itself" means [tex]\( 3n \)[/tex].
- "15 less than three times itself" means [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is added to this expression, so we have: [tex]\( n + (3n - 15) \)[/tex].
- The result is 101, so the equation becomes:
[tex]\[ n + (3n - 15) = 101 \][/tex]
2. Simplify the equation:
- Combine like terms: [tex]\( n + 3n \)[/tex] becomes [tex]\( 4n \)[/tex].
- So the equation simplifies to:
[tex]\[ 4n - 15 = 101 \][/tex]
3. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
The correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
And solving this equation as shown above, we find that [tex]\( n \)[/tex] is 29.
