Answer :
Sure, let's solve the problem step by step:
1. We need to find a number [tex]\( n \)[/tex].
2. The problem states: "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself."
3. We can break this down into two parts:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
4. The number [tex]\( n \)[/tex] is then added to [tex]\( 3n - 15 \)[/tex], which gives us the expression [tex]\( n + (3n - 15) \)[/tex].
5. According to the problem, this sum equals 101.
6. Putting it into an equation form:
[tex]\[
n + (3n - 15) = 101
\][/tex]
7. Combining like terms in the equation:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
8. Solving for [tex]\( n \)[/tex]:
- First, add 15 to both sides of the equation 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:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
So, the equation that we used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
This corresponds to the first option given in the problem:
[tex]\[
3n - 15 + n = 101
\][/tex]
1. We need to find a number [tex]\( n \)[/tex].
2. The problem states: "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself."
3. We can break this down into two parts:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
4. The number [tex]\( n \)[/tex] is then added to [tex]\( 3n - 15 \)[/tex], which gives us the expression [tex]\( n + (3n - 15) \)[/tex].
5. According to the problem, this sum equals 101.
6. Putting it into an equation form:
[tex]\[
n + (3n - 15) = 101
\][/tex]
7. Combining like terms in the equation:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
8. Solving for [tex]\( n \)[/tex]:
- First, add 15 to both sides of the equation 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:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
So, the equation that we used to find the value of [tex]\( n \)[/tex] is:
[tex]\[
3n - 15 + n = 101
\][/tex]
This corresponds to the first option given in the problem:
[tex]\[
3n - 15 + n = 101
\][/tex]
