A thief uses a bag of sand to replace a gold statue that sits on a weight-sensitive, alarmed pedestal. The bag of sand and the statue have exactly the same volume, 1.55 L . (Assume that the mass of the bag is negligible.) Calculate the mass of each object

Let the mass of the gold statue be x. Then, we can use the formula for density, which is mass divided by volume, to set up two equations: Density of gold = x/1.55 Density of sand = m/1.55 where m is the mass of the bag of sand. We know that the volume of the bag of sand and the gold statue are the same, so we can set their densities equal to each other: x/1.55 = m/1.55(3.00) Simplifying this equation, we get: x = m(19.3/3.00) Now, because the thief replaced the gold statue with a bag of sand, the weight on the pedestal should remain the same. Therefore, the mass of the bag of sand and the mass of the gold statue should also be the same. We can set up another equation: x = m Substituting x = m(19.3/3.00) into x = m, we get: m(19.3/3.00) = m Simplifying this equation, we get: m = 1.55(3.00/19.3) m ? 0.24 kg So the mass of the bag of sand is \approx imately 0.24 kg. Using x = m(19.3/3.00), we can find the mass of the gold statue: x = 0.24(19.3/3.00) x ? 1.54 kg So the mass of the gold statue is \approx imately 1.54 kg.