Answer :
We start by translating the problem statement into an equation. The problem states:
"A number, [tex]$n$[/tex], is added to 15 less than 3 times itself. The result is 101."
1. "3 times itself" means multiplying [tex]$n$[/tex] by 3, which gives [tex]$3n$[/tex].
2. "15 less than 3 times itself" means subtracting 15 from [tex]$3n$[/tex], so we write this as [tex]$3n - 15$[/tex].
3. "A number, [tex]$n$[/tex], is added to 15 less than 3 times itself" means we add [tex]$n$[/tex] to [tex]$(3n - 15)$[/tex]:
[tex]$$ n + (3n - 15) = 101. $$[/tex]
4. This equation can be combined by adding the like terms [tex]$n$[/tex] and [tex]$3n$[/tex]:
[tex]$$ 4n - 15 = 101. $$[/tex]
5. To solve for [tex]$n$[/tex], we would add 15 to both sides:
[tex]$$ 4n = 116, $$[/tex]
and then divide by 4:
[tex]$$ n = \frac{116}{4} = 29. $$[/tex]
Among the multiple-choice options, the equation that corresponds to our work is:
[tex]$$ 3n - 15 + n = 101. $$[/tex]
Therefore, the correct equation is the one given by option 1.
"A number, [tex]$n$[/tex], is added to 15 less than 3 times itself. The result is 101."
1. "3 times itself" means multiplying [tex]$n$[/tex] by 3, which gives [tex]$3n$[/tex].
2. "15 less than 3 times itself" means subtracting 15 from [tex]$3n$[/tex], so we write this as [tex]$3n - 15$[/tex].
3. "A number, [tex]$n$[/tex], is added to 15 less than 3 times itself" means we add [tex]$n$[/tex] to [tex]$(3n - 15)$[/tex]:
[tex]$$ n + (3n - 15) = 101. $$[/tex]
4. This equation can be combined by adding the like terms [tex]$n$[/tex] and [tex]$3n$[/tex]:
[tex]$$ 4n - 15 = 101. $$[/tex]
5. To solve for [tex]$n$[/tex], we would add 15 to both sides:
[tex]$$ 4n = 116, $$[/tex]
and then divide by 4:
[tex]$$ n = \frac{116}{4} = 29. $$[/tex]
Among the multiple-choice options, the equation that corresponds to our work is:
[tex]$$ 3n - 15 + n = 101. $$[/tex]
Therefore, the correct equation is the one given by option 1.
