Answer :
To solve the problem, we need to set up an equation based on the given information. The problem states:
1. A number, [tex]\( n \)[/tex], is added to 15 less than 3 times the number itself.
2. The result is 101.
We can translate this into an equation:
- Start by expressing "3 times the number" as [tex]\( 3n \)[/tex].
- "15 less than 3 times the number" can be written as [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is added to this expression, giving us: [tex]\( n + (3n - 15) \)[/tex].
The entire expression equals 101:
[tex]\[ n + (3n - 15) = 101 \][/tex]
Now, let's combine like terms:
1. Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex]: [tex]\( n + 3n = 4n \)[/tex].
2. So, the equation becomes:
[tex]\[ 4n - 15 = 101 \][/tex]
Next, solve for [tex]\( n \)[/tex]:
1. Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
2. Finally, divide both sides by 4 to find the value of [tex]\( n \)[/tex]:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
Therefore, the value of [tex]\( n \)[/tex] is 29. The equation that can be used to find [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This corresponds to the first option: [tex]\( 3n - 15 + n = 101 \)[/tex].
1. A number, [tex]\( n \)[/tex], is added to 15 less than 3 times the number itself.
2. The result is 101.
We can translate this into an equation:
- Start by expressing "3 times the number" as [tex]\( 3n \)[/tex].
- "15 less than 3 times the number" can be written as [tex]\( 3n - 15 \)[/tex].
- The number [tex]\( n \)[/tex] is added to this expression, giving us: [tex]\( n + (3n - 15) \)[/tex].
The entire expression equals 101:
[tex]\[ n + (3n - 15) = 101 \][/tex]
Now, let's combine like terms:
1. Combine [tex]\( n \)[/tex] and [tex]\( 3n \)[/tex]: [tex]\( n + 3n = 4n \)[/tex].
2. So, the equation becomes:
[tex]\[ 4n - 15 = 101 \][/tex]
Next, solve for [tex]\( n \)[/tex]:
1. Add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
2. Finally, divide both sides by 4 to find the value of [tex]\( n \)[/tex]:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
Therefore, the value of [tex]\( n \)[/tex] is 29. The equation that can be used to find [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This corresponds to the first option: [tex]\( 3n - 15 + n = 101 \)[/tex].
