Gold is alloyed (mixed) with other metals to increase its hardness in making
jewelry. (a) Consider a piece of gold jewelry that weighs \(9.85 \mathrm{~g}\)
and has a volume of \(0.675 \mathrm{~cm}^{3}\). The jewelry contains only gold
and silver, which have densities of \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\) and
\(10.5 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. If the total volume of the
jewelry is the sum of the volumes of the gold and silver that it contains,
calculate the percentage of gold (by mass) in the jewelry. (b) The relative
amount of gold in an alloy is commonly expressed in units of karats. Pure gold
is 24 -karat, and the percentage of gold in an alloy is given as a percentage
of this value. For example, an alloy that is \(50 \%\) gold is 12 -karat. State
the purity of the gold jewelry in karats.