Let's work through this word problem step-by-step to determine the correct position of the gopher and to check if Miles' answer is accurate.
1. Understanding the initial condition:
- The gopher is digging 8 inches below the ground surface.
- This means the initial position of the gopher is at -8 inches relative to the surface.
2. Analyzing the next action:
- To avoid a tree root, the gopher digs 3 inches deeper.
- Digging deeper means the gopher will move further down from its initial position.
3. Calculating the new position:
- Since the gopher is moving deeper, we need to add 3 inches to the initial position below ground.
- Since the initial position is -8 inches and it moves 3 inches deeper, we perform the subtraction: [tex]\(-8 - 3\)[/tex].
4. Performing the subtraction:
- [tex]\(-8 - 3 = -11\)[/tex].
5. Interpreting the final position:
- The gopher's new position is -11 inches relative to the ground surface.
6. Evaluating Miles' calculation:
- Miles calculated that the gopher's new position is -11 inches.
- We also calculated and found that the gopher’s new position is indeed -11 inches.
- Therefore, Miles' calculation is correct.
Conclusion:
Miles is correct. The answer should be -11 inches, not -5 inches. The confusion might have arisen from misunderstanding how depth increment works in negative values. But indeed, -11 inches is the correct final position of the gopher relative to the surface.
