Answer :
Sure, let's solve this problem step by step.
1. Let [tex]\( n \)[/tex] be the unknown number.
2. According to the problem, "a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself."
We can break this down as:
- "3 times itself" can be written as [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" can be written as [tex]\( 3n - 15 \)[/tex].
3. When we add [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex], it should equal 101. So, our equation is:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Now, simplify this equation:
[tex]\[
n + 3n - 15 = 101
\][/tex]
5. Combine the like terms:
[tex]\[
4n - 15 = 101
\][/tex]
6. To isolate [tex]\( n \)[/tex], add 15 to both sides of the equation:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
7. Divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
So, the equation used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
1. Let [tex]\( n \)[/tex] be the unknown number.
2. According to the problem, "a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself."
We can break this down as:
- "3 times itself" can be written as [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" can be written as [tex]\( 3n - 15 \)[/tex].
3. When we add [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex], it should equal 101. So, our equation is:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Now, simplify this equation:
[tex]\[
n + 3n - 15 = 101
\][/tex]
5. Combine the like terms:
[tex]\[
4n - 15 = 101
\][/tex]
6. To isolate [tex]\( n \)[/tex], add 15 to both sides of the equation:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
7. Divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
So, the equation used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
3n - 15 + n = 101
\][/tex]
