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The Composition of Gold

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You have a piece of gold jewelry weighing 8.5 grams. Its volume is 0.64 cubic centimeters. Assume that th metal is an alloy of gold and copper, which have densities of 19.3 g/cm^3 and 8.5 g/cm^3 respectively. Also assume that there are no changes in volume when the metals are mixed. First, calculate the percentage of gold by volume. Next, calculate the percentage of gold by mass in the piece of jewelry. The relative amount of gold by mass is measured in karats. Pure gold is 24 karat gold. An alloy that is 50% (by mass) gold is 12 karats. State the composition of gold in the jewelry in karats.

a. 17.6 karats
b. 15.4 karats
c. 16.8k
d. 11.2 karats
e. 18.9 karats.

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Solution Preview

First: let x = volume of gold and y = volume of copper. We will form 2 equations:
x + y = 0.64
19.3x + 8.5y = 8.5

Using substitution y = 0.64-x ...

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