Answer :
To solve the problem, we need to set up an equation based on the information given:
1. A number [tex]\( n \)[/tex] is added to "15 less than 3 times itself." This means:
- First, we find "3 times the number," which is [tex]\( 3n \)[/tex].
- Then, "15 less than 3 times the number" is [tex]\( 3n - 15 \)[/tex].
2. The number [tex]\( n \)[/tex] is added to this expression, resulting in 101. So, our equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the equation:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex].
- The equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
4. Solve for [tex]\( n \)[/tex]:
- First, add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Next, divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
Based on these steps, the correct equation from the options given is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
Therefore, the number [tex]\( n \)[/tex] is 29.
1. A number [tex]\( n \)[/tex] is added to "15 less than 3 times itself." This means:
- First, we find "3 times the number," which is [tex]\( 3n \)[/tex].
- Then, "15 less than 3 times the number" is [tex]\( 3n - 15 \)[/tex].
2. The number [tex]\( n \)[/tex] is added to this expression, resulting in 101. So, our equation becomes:
[tex]\[
n + (3n - 15) = 101
\][/tex]
3. Simplify the equation:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex].
- The equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
4. Solve for [tex]\( n \)[/tex]:
- First, add 15 to both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Next, divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
Based on these steps, the correct equation from the options given is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
Therefore, the number [tex]\( n \)[/tex] is 29.
