Answer :
To determine which situations could match the formula [tex]\(500 = 100x\)[/tex], let's consider each option and see if it fits.
### Understanding the Formula
The equation [tex]\(500 = 100x\)[/tex] implies some relationship between 500, 100, and an unknown variable [tex]\(x\)[/tex]. This can be interpreted as:
- Total = Rate × Quantity (or time).
- Here, 500 is the total, 100 is the constant factor (rate), and [tex]\(x\)[/tex] is what we're solving for.
### Evaluating Each Situation
1. An object travels 500 feet for 100 seconds.
- Here, [tex]\(500\)[/tex] represents the distance in feet, and [tex]\(100\)[/tex] is the time in seconds.
- Solving [tex]\(500 = 100x\)[/tex], we find [tex]\(x = \frac{500}{100} = 5\)[/tex].
- This means the speed is 5 feet per second.
2. An object travels at 500 miles per hour for 100 hours.
- Here, [tex]\(500\)[/tex] is the speed (rate) in miles per hour, and [tex]\(100\)[/tex] is the time in hours.
- Solving [tex]\(500 = 100x\)[/tex], we find [tex]\(x = \frac{500}{100} = 5\)[/tex].
- This calculation doesn't relate logically as the formula involves defining miles in terms of time or speed, which is not coherent with these units.
3. An object travels 10 inches per minute for 500 minutes.
- Here, [tex]\(10\)[/tex] is the speed (rate) in inches per minute, and [tex]\(500\)[/tex] is the total time in minutes.
- Solving [tex]\(500 = 10x\)[/tex], we find [tex]\(x = \frac{500}{10} = 50\)[/tex].
- This doesn’t match our formula [tex]\(500 = 100x\)[/tex], which requires [tex]\(x\)[/tex] to be 5 or 50 in this context.
4. An object travels 500 miles at a rate of 100 miles per hour.
- Here, [tex]\(500\)[/tex] is the distance in miles, and [tex]\(100\)[/tex] is the rate or speed in miles per hour.
- Solving [tex]\(500 = 100x\)[/tex], we find [tex]\(x = \frac{500}{100} = 5\)[/tex].
- This means the time taken is 5 hours, which correctly matches the original formula.
### Conclusion
The situations that match the formula [tex]\(500 = 100x\)[/tex] are:
- An object travels 500 feet for 100 seconds with the interpretation that the speed is 5 feet per second.
- An object travels 500 miles at a rate of 100 miles per hour which implies the time is 5 hours.
These two scenarios align with the formula by understanding the relationship between distance, rate, and time.
### Understanding the Formula
The equation [tex]\(500 = 100x\)[/tex] implies some relationship between 500, 100, and an unknown variable [tex]\(x\)[/tex]. This can be interpreted as:
- Total = Rate × Quantity (or time).
- Here, 500 is the total, 100 is the constant factor (rate), and [tex]\(x\)[/tex] is what we're solving for.
### Evaluating Each Situation
1. An object travels 500 feet for 100 seconds.
- Here, [tex]\(500\)[/tex] represents the distance in feet, and [tex]\(100\)[/tex] is the time in seconds.
- Solving [tex]\(500 = 100x\)[/tex], we find [tex]\(x = \frac{500}{100} = 5\)[/tex].
- This means the speed is 5 feet per second.
2. An object travels at 500 miles per hour for 100 hours.
- Here, [tex]\(500\)[/tex] is the speed (rate) in miles per hour, and [tex]\(100\)[/tex] is the time in hours.
- Solving [tex]\(500 = 100x\)[/tex], we find [tex]\(x = \frac{500}{100} = 5\)[/tex].
- This calculation doesn't relate logically as the formula involves defining miles in terms of time or speed, which is not coherent with these units.
3. An object travels 10 inches per minute for 500 minutes.
- Here, [tex]\(10\)[/tex] is the speed (rate) in inches per minute, and [tex]\(500\)[/tex] is the total time in minutes.
- Solving [tex]\(500 = 10x\)[/tex], we find [tex]\(x = \frac{500}{10} = 50\)[/tex].
- This doesn’t match our formula [tex]\(500 = 100x\)[/tex], which requires [tex]\(x\)[/tex] to be 5 or 50 in this context.
4. An object travels 500 miles at a rate of 100 miles per hour.
- Here, [tex]\(500\)[/tex] is the distance in miles, and [tex]\(100\)[/tex] is the rate or speed in miles per hour.
- Solving [tex]\(500 = 100x\)[/tex], we find [tex]\(x = \frac{500}{100} = 5\)[/tex].
- This means the time taken is 5 hours, which correctly matches the original formula.
### Conclusion
The situations that match the formula [tex]\(500 = 100x\)[/tex] are:
- An object travels 500 feet for 100 seconds with the interpretation that the speed is 5 feet per second.
- An object travels 500 miles at a rate of 100 miles per hour which implies the time is 5 hours.
These two scenarios align with the formula by understanding the relationship between distance, rate, and time.
