Let's solve the problem step-by-step to determine the relationship between the original number and the final number.
1. First, let's denote the original number as [tex]\( x \)[/tex].
2. We need to examine four possible relationships between [tex]\( x \)[/tex] and the final number [tex]\( y \)[/tex]:
- Option A: The final number is [tex]\(\frac{1}{3}\)[/tex] of the original number.
- Mathematically, [tex]\( y = \frac{x}{3} \)[/tex]
- Option B: The final number is 3 times the original number.
- Mathematically, [tex]\( y = 3x \)[/tex]
- Option C: The final number is the same as the original number.
- Mathematically, [tex]\( y = x \)[/tex]
- Option D: The final number is 10 more than the original number.
- Mathematically, [tex]\( y = x + 10 \)[/tex]
3. Let's use an example where the original number [tex]\( x = 10 \)[/tex]. We need to determine which of these options correctly follows from our known relationship.
- Option A: If [tex]\( x = 10 \)[/tex], then [tex]\( y = \frac{10}{3} \approx 3.33 \)[/tex]
- Option B: If [tex]\( x = 10 \)[/tex], then [tex]\( y = 3 \times 10 = 30 \)[/tex]
- Option C: If [tex]\( x = 10 \)[/tex], then [tex]\( y = 10 \)[/tex]
- Option D: If [tex]\( x = 10 \)[/tex], then [tex]\( y = 10 + 10 = 20 \)[/tex]
4. Comparing these results to determine which matches our condition, we see:
- Option A gives us [tex]\( y \approx 3.33 \)[/tex]
- Option B gives us [tex]\( y = 30 \)[/tex]
- Option C gives us [tex]\( y = 10 \)[/tex]
- Option D gives us [tex]\( y = 20 \)[/tex]
Given the relationship where the final number is 3 times the original number, as illustrated:
The correct relationship is Option B: The final number is 3 times the original number.
