MATH HW HELP NEEDED ASAP

Question

In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 68.2 grams.

I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.

Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?

Answer 1

Assuming that the unknown, blended metal has a density of exactly 9.7 g/ml, we can set up a system of equations to find the answer. Let x be the volume of gold in mL and y be the volume of the other metal in mL.

19.3x + 9.7y = 68.2

x + y = 5

When we solve this equation, we get that x = 197/96. Since this quantity is a volume in mL, we can multiply it with the density to get the mass: (197 * 19.3)/96 = 39.6052.

To find the percentage of gold, we divide the mass of the gold by the mass of the chain and multiply by 100: (39.6052 / 68.2) * 100 = 58.07% gold by mass.