College

A number, [tex] n [/tex], is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of [tex] n [/tex]?

A. [tex] 3n - 15 + n = 101 [/tex]

B. [tex] 3n + 15 + n = 101 [/tex]

C. [tex] 3n - 15 - n = 101 [/tex]

D. [tex] 3n + 15 - n = 101 [/tex]

Answer :

Alright, let's solve the problem step-by-step.

We are given the following information:

1. A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself.
2. The result is 101.

Let's break this down into an equation.

### Step 1: Define the Expression
- "3 times itself" is [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" is [tex]\( 3n - 15 \)[/tex].

### Step 2: Create the Equation
- The number [tex]\( n \)[/tex] is added to [tex]\( 3n - 15 \)[/tex]:
[tex]\[
n + (3n - 15)
\][/tex]

### Step 3: Set Up the Equation
- This sum should be equal to 101:
[tex]\[
n + (3n - 15) = 101
\][/tex]

### Step 4: Simplify the Equation
- Combine like terms on the left side:
[tex]\[
n + 3n - 15 = 101
\][/tex]
[tex]\[
4n - 15 = 101
\][/tex]

### Step 5: Solve for [tex]\( n \)[/tex]
- Add 15 to both sides:
[tex]\[
4n - 15 + 15 = 101 + 15
\][/tex]
[tex]\[
4n = 116
\][/tex]

- Divide by 4:
[tex]\[
n = \frac{116}{4}
\][/tex]
[tex]\[
n = 29
\][/tex]

So, the equation to find the value of [tex]\( n \)[/tex] is:
[tex]\[
4n - 15 = 101
\][/tex]

Let's verify our equation choices to find a match:
- [tex]$3n - 15 + n = 101$[/tex]

This equation is correct as it simplifies to [tex]\( 4n - 15 = 101 \)[/tex].

Therefore, the correct equation is:

[tex]\[
3n - 15 + n = 101
\][/tex]

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