Answer :
To solve the problem, we need to find a number [tex]\( n \)[/tex] that, when added to 15 less than 3 times itself, gives a result of 101. Let's break it down step-by-step:
1. Understand the problem: We are told that a number [tex]\( n \)[/tex] is added to something else. The "something else" is described as "15 less than 3 times itself." So, let's express each part mathematically.
2. Express '15 less than 3 times itself':
- "3 times itself" means multiplying the number [tex]\( n \)[/tex] by 3, which is [tex]\( 3n \)[/tex].
- "15 less than that" means we subtract 15 from [tex]\( 3n \)[/tex], resulting in [tex]\( 3n - 15 \)[/tex].
3. Set up the equation: According to the problem, when you add the number [tex]\( n \)[/tex] to this quantity, the result is 101. So we form the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplify the equation: Combine like terms.
- [tex]\( n + 3n \)[/tex] gives us [tex]\( 4n \)[/tex].
- The equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
5. Solve the equation 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]
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
1. Understand the problem: We are told that a number [tex]\( n \)[/tex] is added to something else. The "something else" is described as "15 less than 3 times itself." So, let's express each part mathematically.
2. Express '15 less than 3 times itself':
- "3 times itself" means multiplying the number [tex]\( n \)[/tex] by 3, which is [tex]\( 3n \)[/tex].
- "15 less than that" means we subtract 15 from [tex]\( 3n \)[/tex], resulting in [tex]\( 3n - 15 \)[/tex].
3. Set up the equation: According to the problem, when you add the number [tex]\( n \)[/tex] to this quantity, the result is 101. So we form the equation:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplify the equation: Combine like terms.
- [tex]\( n + 3n \)[/tex] gives us [tex]\( 4n \)[/tex].
- The equation becomes [tex]\( 4n - 15 = 101 \)[/tex].
5. Solve the equation 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]
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
