Gold Value Calculation: Unveiling the Treasure in a Bracelet

How can we determine the value of gold in a bracelet?

Given the mass of the bracelet, the scale reading when submerged in water, and the densities of gold and copper, how do we calculate the value of the gold in the bracelet?

Calculating the Value of Gold in the Bracelet

To determine the value of the gold in the bracelet, we need to follow a series of steps based on the given data. Let's break it down:

Firstly, we know that the scale reads 58.9 grams when the bracelet is submerged in water. This reading represents the weight of the water displaced by the bracelet, which is equivalent to the buoyant force acting on it. Since the density of water is 1 g/cc, we can use the weight of the water displaced to find the volume of the bracelet, which is equal to 58.9 cc.

Next, we calculate the volume of gold in the bracelet using the density of gold, which is 19.3 g/cc. By multiplying the volume of the bracelet by the density of gold, we find that the mass of gold in the bracelet is 1137.77 grams.

Finally, we determine the value of the gold by multiplying the mass of gold by the current price of gold, which is $57.60 per gram. The calculation yields a value of $65,456.39 for the gold contained in the bracelet.

Therefore, the treasure hidden in the bracelet is worth approximately $65,456.39, a gleaming testament to the valuable composition of this exquisite piece of jewelry.