Answer :
Let's go through the problem step by step.
1. The phrase “15 less than 3 times itself” means we first multiply the number [tex]$n$[/tex] by 3 and then subtract 15. This gives us the expression:
[tex]$$
3n - 15.
$$[/tex]
2. The number [tex]$n$[/tex] is added to this expression, so we have:
[tex]$$
n + (3n - 15).
$$[/tex]
3. According to the problem, the result is equal to 101. Therefore, the equation becomes:
[tex]$$
n + (3n - 15) = 101.
$$[/tex]
4. Simplify the left-hand side by combining like terms:
[tex]$$
n + 3n - 15 = 4n - 15.
$$[/tex]
5. The simplified equation is:
[tex]$$
4n - 15 = 101.
$$[/tex]
Thus, the equation that can be used to find the value of [tex]$n$[/tex] is:
[tex]$$
3n - 15 + n = 101.
$$[/tex]
6. Solving the equation:
- Add the [tex]$n$[/tex] terms: [tex]$4n - 15 = 101$[/tex].
- Add 15 to both sides:
[tex]$$
4n = 101 + 15 = 116.
$$[/tex]
- Divide by 4:
[tex]$$
n = \frac{116}{4} = 29.
$$[/tex]
Therefore, the correct multiple-choice option is:
[tex]$$
\boxed{3n - 15 + n = 101.}
$$[/tex]
1. The phrase “15 less than 3 times itself” means we first multiply the number [tex]$n$[/tex] by 3 and then subtract 15. This gives us the expression:
[tex]$$
3n - 15.
$$[/tex]
2. The number [tex]$n$[/tex] is added to this expression, so we have:
[tex]$$
n + (3n - 15).
$$[/tex]
3. According to the problem, the result is equal to 101. Therefore, the equation becomes:
[tex]$$
n + (3n - 15) = 101.
$$[/tex]
4. Simplify the left-hand side by combining like terms:
[tex]$$
n + 3n - 15 = 4n - 15.
$$[/tex]
5. The simplified equation is:
[tex]$$
4n - 15 = 101.
$$[/tex]
Thus, the equation that can be used to find the value of [tex]$n$[/tex] is:
[tex]$$
3n - 15 + n = 101.
$$[/tex]
6. Solving the equation:
- Add the [tex]$n$[/tex] terms: [tex]$4n - 15 = 101$[/tex].
- Add 15 to both sides:
[tex]$$
4n = 101 + 15 = 116.
$$[/tex]
- Divide by 4:
[tex]$$
n = \frac{116}{4} = 29.
$$[/tex]
Therefore, the correct multiple-choice option is:
[tex]$$
\boxed{3n - 15 + n = 101.}
$$[/tex]
