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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]


Sagot :

To solve the problem, let's break it down step by step.

1. Understanding the Problem:
- We have a number [tex]\( n \)[/tex].
- "3 times itself" refers to [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" translates to [tex]\( 3n - 15 \)[/tex].
- Adding the number [tex]\( n \)[/tex] and [tex]\( 15 \)[/tex] less than 3 times itself gives [tex]\( n + (3n - 15) \)[/tex].
- According to the problem, this sum is equal to 101.

2. Formulating the Equation:
- Now, we can write the equation based on the given information:
[tex]\[ n + (3n - 15) = 101 \][/tex]

3. Simplifying the Equation:
- Combine like terms on the left-hand side of the equation:
[tex]\[ n + 3n - 15 = 101 \][/tex]
[tex]\[ 4n - 15 = 101 \][/tex]

4. Solving the Equation:
- 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]
- Then, divide both sides by 4 to solve for [tex]\( n \)[/tex]:
[tex]\[ \frac{4n}{4} = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]

5. Matching the Equation:
- The simplified form of the equation [tex]\( n + (3n - 15) = 101 \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
- Thus, the correct equation that matches the problem statement is:
[tex]\[ 3n - 15 + n = 101 \][/tex]

Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]