Answer :
We start by translating the phrase into an equation. The expression “15 less than 3 times itself” means you take 3 times the number [tex]$n$[/tex] and then subtract 15, giving:
[tex]$$3n - 15$$[/tex]
Then, a number [tex]$n$[/tex] is added to this expression:
[tex]$$n + (3n - 15)$$[/tex]
This sum is equal to 101:
[tex]$$n + (3n - 15) = 101$$[/tex]
We can rearrange the terms to obtain:
[tex]$$3n - 15 + n = 101$$[/tex]
This corresponds to the first option.
Now, let’s solve the equation step by step.
1. Combine like terms:
[tex]$$
3n + n = 4n, \quad \text{so the equation becomes} \quad 4n - 15 = 101.
$$[/tex]
2. Add 15 to both sides to isolate the term with [tex]$n$[/tex]:
[tex]$$
4n - 15 + 15 = 101 + 15 \quad \Rightarrow \quad 4n = 116.
$$[/tex]
3. Divide both sides by 4 to solve for [tex]$n$[/tex]:
[tex]$$
n = \frac{116}{4} = 29.
$$[/tex]
Thus, the equation used to find the value of [tex]$n$[/tex] is
[tex]$$3n - 15 + n = 101,$$[/tex]
and solving it gives [tex]$n = 29$[/tex].
[tex]$$3n - 15$$[/tex]
Then, a number [tex]$n$[/tex] is added to this expression:
[tex]$$n + (3n - 15)$$[/tex]
This sum is equal to 101:
[tex]$$n + (3n - 15) = 101$$[/tex]
We can rearrange the terms to obtain:
[tex]$$3n - 15 + n = 101$$[/tex]
This corresponds to the first option.
Now, let’s solve the equation step by step.
1. Combine like terms:
[tex]$$
3n + n = 4n, \quad \text{so the equation becomes} \quad 4n - 15 = 101.
$$[/tex]
2. Add 15 to both sides to isolate the term with [tex]$n$[/tex]:
[tex]$$
4n - 15 + 15 = 101 + 15 \quad \Rightarrow \quad 4n = 116.
$$[/tex]
3. Divide both sides by 4 to solve for [tex]$n$[/tex]:
[tex]$$
n = \frac{116}{4} = 29.
$$[/tex]
Thus, the equation used to find the value of [tex]$n$[/tex] is
[tex]$$3n - 15 + n = 101,$$[/tex]
and solving it gives [tex]$n = 29$[/tex].
