Answer :
To determine which situations could match the formula [tex]\(500 = 100 \times x\)[/tex], we need to understand what this equation represents. Here, [tex]\(x\)[/tex] is a variable, and the equation can be interpreted as describing a relationship between different measurements, such as time, speed, or distance.
Let's look at each situation:
1. An object travels 100 inches per minute for 500 minutes.
- Distance traveled = rate × time = [tex]\(100 \text{ inches/min} \times 500 \text{ min} = 50000 \text{ inches}\)[/tex].
- This equation doesn't directly connect to [tex]\(500 = 100 \times x\)[/tex], where the right side equals 5000, but it doesn't define [tex]\(x\)[/tex]. So, this statement doesn't fully match.
2. An object travels 500 feet for 100 seconds.
- Here, the distance is 500 feet, and we would look for the rate: 500 feet = 100 × [tex]\(x\)[/tex].
- Solving for [tex]\(x\)[/tex], you get [tex]\(x = 500 / 100 = 5\)[/tex].
- This matches the condition where the left side is 500, and the right side's relationship [tex]\(100 \times x\)[/tex] is fulfilled with [tex]\(x = 5\)[/tex].
3. An object travels at 500 miles per hour for 100 hours.
- Distance traveled = speed × time = [tex]\(500 \text{ miles/hr} \times 100 \text{ hrs} = 50000 \text{ miles}\)[/tex].
- Like in the first case, while this calculation gives us a large number, it doesn’t relate to a simple solution using the original formula [tex]\(500 = 100 \times x\)[/tex].
4. An object travels 500 miles at a rate of 100 miles per hour.
- Time taken = distance / speed = [tex]\(500 \text{ miles} / 100 \text{ miles/hr} = 5 \text{ hours}\)[/tex].
- Here, we have [tex]\(x = 5\)[/tex], matching the equation [tex]\(500 = 100 \times x\)[/tex] because [tex]\(500 = 100 \times 5\)[/tex].
Considering these interpretations:
- Situation 2 and Situation 4 can match the formula [tex]\(500 = 100 \times x\)[/tex], where [tex]\(x\)[/tex] is effectively representing time or another measurable quantity that fits the formula.
Let's look at each situation:
1. An object travels 100 inches per minute for 500 minutes.
- Distance traveled = rate × time = [tex]\(100 \text{ inches/min} \times 500 \text{ min} = 50000 \text{ inches}\)[/tex].
- This equation doesn't directly connect to [tex]\(500 = 100 \times x\)[/tex], where the right side equals 5000, but it doesn't define [tex]\(x\)[/tex]. So, this statement doesn't fully match.
2. An object travels 500 feet for 100 seconds.
- Here, the distance is 500 feet, and we would look for the rate: 500 feet = 100 × [tex]\(x\)[/tex].
- Solving for [tex]\(x\)[/tex], you get [tex]\(x = 500 / 100 = 5\)[/tex].
- This matches the condition where the left side is 500, and the right side's relationship [tex]\(100 \times x\)[/tex] is fulfilled with [tex]\(x = 5\)[/tex].
3. An object travels at 500 miles per hour for 100 hours.
- Distance traveled = speed × time = [tex]\(500 \text{ miles/hr} \times 100 \text{ hrs} = 50000 \text{ miles}\)[/tex].
- Like in the first case, while this calculation gives us a large number, it doesn’t relate to a simple solution using the original formula [tex]\(500 = 100 \times x\)[/tex].
4. An object travels 500 miles at a rate of 100 miles per hour.
- Time taken = distance / speed = [tex]\(500 \text{ miles} / 100 \text{ miles/hr} = 5 \text{ hours}\)[/tex].
- Here, we have [tex]\(x = 5\)[/tex], matching the equation [tex]\(500 = 100 \times x\)[/tex] because [tex]\(500 = 100 \times 5\)[/tex].
Considering these interpretations:
- Situation 2 and Situation 4 can match the formula [tex]\(500 = 100 \times x\)[/tex], where [tex]\(x\)[/tex] is effectively representing time or another measurable quantity that fits the formula.
