Answer :
We are told that a number [tex]$n$[/tex] is added to “15 less than 3 times itself.” The phrase “15 less than 3 times itself” means we take [tex]$3n$[/tex] and subtract 15, giving us [tex]$3n - 15$[/tex]. Therefore, when we add the number [tex]$n$[/tex] to this expression, the resulting equation is:
[tex]$$3n - 15 + n = 101.$$[/tex]
Now, let’s simplify the left-hand side by combining like terms. The [tex]$n$[/tex] and [tex]$3n$[/tex] combine to give [tex]$4n$[/tex], so the equation becomes:
[tex]$$4n - 15 = 101.$$[/tex]
Next, add 15 to both sides to isolate the term with [tex]$n$[/tex]:
[tex]$$4n = 101 + 15 = 116.$$[/tex]
Finally, divide both sides by 4 to solve for [tex]$n$[/tex]:
[tex]$$n = \frac{116}{4} = 29.$$[/tex]
Thus, the correct equation to find [tex]$n$[/tex] is:
[tex]$$\boxed{3n - 15 + n = 101.}$$[/tex]
[tex]$$3n - 15 + n = 101.$$[/tex]
Now, let’s simplify the left-hand side by combining like terms. The [tex]$n$[/tex] and [tex]$3n$[/tex] combine to give [tex]$4n$[/tex], so the equation becomes:
[tex]$$4n - 15 = 101.$$[/tex]
Next, add 15 to both sides to isolate the term with [tex]$n$[/tex]:
[tex]$$4n = 101 + 15 = 116.$$[/tex]
Finally, divide both sides by 4 to solve for [tex]$n$[/tex]:
[tex]$$n = \frac{116}{4} = 29.$$[/tex]
Thus, the correct equation to find [tex]$n$[/tex] is:
[tex]$$\boxed{3n - 15 + n = 101.}$$[/tex]
