Determine Reasonableness of solutions practice
To determine the reasonableness of solutions, we need to consider the context of the problem and whether the solutions make sense in that context. Here are a few practice problems to help you practice determining the reasonableness of solutions:
1. Problem: A car traveled 250 miles in 2.5 hours. What was the average speed of the car?
Solution: To find the average speed, we divide the distance by the time: 250 miles / 2.5 hours = 100 miles per hour.
Reasonableness: In this case, a car traveling at an average speed of 100 miles per hour is reasonable as it falls within the typical range of speeds for cars on highways.
2. Problem: A store is selling a shirt for $150, and it has a 20% discount. What is the final price of the shirt after the discount?
Solution: To find the final price after the discount, we multiply the original price by 1 minus the discount rate: $150 * (1 - 20%) = $150 * 0.8 = $120.
Reasonableness: The final price of $120 after a 20% discount is reasonable for a high-quality shirt. It reflects the expected reduction in price due to the discount.
3. Problem: A company has a production target of 1000 units per hour. They produced 500 units in 0.5 hours. Did they meet their production target?
Solution: To determine if they met their production target, we need to compare the actual production with the target. They produced 500 units in 0.5 hours, which means they produced 1000 units per hour (500 units / 0.5 hours). Therefore, they met their production target.
Reasonableness: The fact that they produced exactly 1000 units per hour, matching their production target, is reasonable and shows that they met their goal.
By considering the context and using common sense, we can determine the reasonableness of solutions in various problems.