Answer :
To solve this problem, let's break down the steps:
1. Understand the problem: We want to find a number [tex]\( n \)[/tex] such that when it is added to 15 less than 3 times itself, the result is 101.
2. Translate the problem into an equation:
- "3 times itself" can be written as [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" is [tex]\( 3n - 15 \)[/tex].
- The sum of [tex]\( n \)[/tex] and "15 less than 3 times itself" is [tex]\( n + (3n - 15) \)[/tex].
3. Set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplify the equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides of the equation:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
6. Verify the solution: Plug [tex]\( n = 29 \)[/tex] back into the context of the original problem:
- Calculate 3 times 29: [tex]\( 3 \times 29 = 87 \)[/tex]
- Calculate 15 less than that: [tex]\( 87 - 15 = 72 \)[/tex]
- Now add 29 to that result: [tex]\( 29 + 72 = 101 \)[/tex], which satisfies the original condition.
Therefore, the correct equation from the choices given is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
And the value of [tex]\( n \)[/tex] is 29.
1. Understand the problem: We want to find a number [tex]\( n \)[/tex] such that when it is added to 15 less than 3 times itself, the result is 101.
2. Translate the problem into an equation:
- "3 times itself" can be written as [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" is [tex]\( 3n - 15 \)[/tex].
- The sum of [tex]\( n \)[/tex] and "15 less than 3 times itself" is [tex]\( n + (3n - 15) \)[/tex].
3. Set up the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplify the equation:
- Combine like terms:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides of the equation:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]
6. Verify the solution: Plug [tex]\( n = 29 \)[/tex] back into the context of the original problem:
- Calculate 3 times 29: [tex]\( 3 \times 29 = 87 \)[/tex]
- Calculate 15 less than that: [tex]\( 87 - 15 = 72 \)[/tex]
- Now add 29 to that result: [tex]\( 29 + 72 = 101 \)[/tex], which satisfies the original condition.
Therefore, the correct equation from the choices given is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
And the value of [tex]\( n \)[/tex] is 29.
