Answer :
Sure! Let's break down the problem step-by-step:
We are given that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself, and the result is 101.
1. Express the given information as an equation:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- Adding [tex]\( n \)[/tex] to this expression gives us [tex]\( (3n - 15) + n \)[/tex].
2. Set up the equation according to the problem statement:
- The result of adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex] is 101:
[tex]\[
(3n - 15) + n = 101
\][/tex]
3. Simplify the equation:
[tex]\[
3n - 15 + n = 101
\][/tex]
4. Combine like terms:
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
- First, isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Then, divide by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
Therefore, the number [tex]\( n \)[/tex] is 29, and the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
\[
3n - 15 + n = 101
\
We are given that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself, and the result is 101.
1. Express the given information as an equation:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- Adding [tex]\( n \)[/tex] to this expression gives us [tex]\( (3n - 15) + n \)[/tex].
2. Set up the equation according to the problem statement:
- The result of adding [tex]\( n \)[/tex] to [tex]\( 3n - 15 \)[/tex] is 101:
[tex]\[
(3n - 15) + n = 101
\][/tex]
3. Simplify the equation:
[tex]\[
3n - 15 + n = 101
\][/tex]
4. Combine like terms:
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
- First, isolate the term with [tex]\( n \)[/tex]:
[tex]\[
4n = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Then, divide by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
Therefore, the number [tex]\( n \)[/tex] is 29, and the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
\[
3n - 15 + n = 101
\
