Answer :
To solve this problem, we need to set up an equation described by the situation and then solve for the number [tex]\( n \)[/tex].
The problem says that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself. This means we start with 3 times the number, subtract 15 from that, and then add [tex]\( n \)[/tex]. The result of this operation is equal to 101.
Let's break down the steps:
1. Express "3 times the number": This would be [tex]\( 3n \)[/tex].
2. Find "15 less than 3 times itself": Subtract 15 from [tex]\( 3n \)[/tex], resulting in [tex]\( 3n - 15 \)[/tex].
3. Add the original number [tex]\( n \)[/tex] to this expression: This results in [tex]\( n + (3n - 15) \)[/tex].
4. Set the whole expression equal to 101:
[tex]\[
n + (3n - 15) = 101
\][/tex]
5. Combine like terms:
- Combine the [tex]\( n \)[/tex] terms: [tex]\( n + 3n = 4n \)[/tex].
- Substitute back into the equation: [tex]\( 4n - 15 = 101 \)[/tex].
6. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate terms with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
Therefore, the equation that can be used to obtain the value of [tex]\( n \)[/tex] is [tex]\( 3n - 15 + n = 101 \)[/tex], and the value of [tex]\( n \)[/tex] is 29.
The problem says that a number [tex]\( n \)[/tex] is added to 15 less than 3 times itself. This means we start with 3 times the number, subtract 15 from that, and then add [tex]\( n \)[/tex]. The result of this operation is equal to 101.
Let's break down the steps:
1. Express "3 times the number": This would be [tex]\( 3n \)[/tex].
2. Find "15 less than 3 times itself": Subtract 15 from [tex]\( 3n \)[/tex], resulting in [tex]\( 3n - 15 \)[/tex].
3. Add the original number [tex]\( n \)[/tex] to this expression: This results in [tex]\( n + (3n - 15) \)[/tex].
4. Set the whole expression equal to 101:
[tex]\[
n + (3n - 15) = 101
\][/tex]
5. Combine like terms:
- Combine the [tex]\( n \)[/tex] terms: [tex]\( n + 3n = 4n \)[/tex].
- Substitute back into the equation: [tex]\( 4n - 15 = 101 \)[/tex].
6. Solve for [tex]\( n \)[/tex]:
- Add 15 to both sides to isolate terms with [tex]\( n \)[/tex]:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]
- Divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{116}{4} = 29
\][/tex]
Therefore, the equation that can be used to obtain the value of [tex]\( n \)[/tex] is [tex]\( 3n - 15 + n = 101 \)[/tex], and the value of [tex]\( n \)[/tex] is 29.
