Question

Sam says the heaviest bean bag is twice as heavy as the lightest bean bag. Amelia says the heaviest bean bag is three times as heavy as the lightest bean bag.

Who is correct? Explain how you know.

Answer 1

Both Sam and Amelia cannot be correct at the same time, as they make contradictory statements about the weight of the heaviest bean bag in comparison to the lightest bean bag.

Let's assume the weight of the lightest bean bag is 'x'. According to Sam, the weight of the heaviest bean bag would be twice as heavy as the lightest bean bag. Therefore, the weight of the heaviest bean bag would be 2x.

On the other hand, Amelia states that the heaviest bean bag is three times as heavy as the lightest bean bag. Therefore, the weight of the heaviest bean bag would be 3x.

Since Sam says the heaviest bean bag is 2x, and Amelia says it is 3x, their statements cannot both be true. Therefore, either Sam or Amelia is incorrect.

In conclusion, we cannot determine who is correct without further information, such as the actual weights of the bean bags.

Answer 2

Without empirical measurements, we cannot determine whether Sam's or Amelia's claim about the weight of the bean bags is correct. The question touches on the mathematics concepts of ratios and comparative weights as well as percent uncertainty.

Step-by-step explanation:

The question related to mathematics, specifically concerning the comparative weight of two bean bags, is best resolved by gathering empirical evidence such as using a scale to measure the actual weights. As the question stands, without measurable data or additional information, it is impossible to definitively confirm whether Sam or Amelia is correct. Both statements cannot be true since the heaviest bean bag cannot be both twice and three times as heavy as the lightest one simultaneously. The concept involved here aligns with understanding ratios and comparative weights.

Discussing percent uncertainty, as indicated in the supplementary information, relates to assessing the reliability of measurements. For instance, if a 5-lb bag of apples has a percent uncertainty of 8%, it implies an uncertainty of 0.4 lbs; should the bag weigh half (2.5 lbs), but the uncertainty amount remains the same, the percent uncertainty would double to 16% (because 0.4 lbs is 16% of 2.5 lbs), demonstrating the inverse relationship between the size of the object and percent uncertainty when the absolute uncertainty remains constant.