Certainly! Let's carefully interpret the given sentence and translate it into a mathematical equation step by step.
Sentence:
"Five more than three times the number is one-third more than the sum of the number and itself."
Step-by-step translation:
1. Part 1: Five more than three times the number
- Let [tex]\( n \)[/tex] represent the number.
- Three times the number is [tex]\( 3n \)[/tex].
- Five more than three times the number is [tex]\( 3n + 5 \)[/tex].
2. Part 2: One-third more than the sum of the number and itself
- The sum of the number and itself is [tex]\( n + n \)[/tex], which simplifies to [tex]\( 2n \)[/tex].
- One-third of this sum would be [tex]\( \frac{1}{3}(2n) \)[/tex].
3. Combining Parts:
- According to the sentence, these two expressions are equal.
- Thus, we set them equal: [tex]\( 3n + 5 = \frac{1}{3}(2n) \)[/tex].
Comparison with provided options:
1. [tex]\( 3n + 5 = \frac{1}{3}(n + n) \)[/tex]
2. [tex]\( 3n + 5 = (n + n) + \frac{1}{3} \)[/tex]
3. [tex]\( 5(3n) = \frac{1}{3}n + n \)[/tex]
4. [tex]\( 5(3n) = \frac{1}{3} + n \)[/tex]
Clearly, the correct equation is option 1:
[tex]\[ 3n + 5 = \frac{1}{3}(n + n) \][/tex]
Therefore, the correct equation that represents the sentence "Five more than three times the number is one-third more than the sum of the number and itself" is option 1:
[tex]\[ \boxed{1} \][/tex]
