Answer
61.51% of Gold.
Work Step by Step
1. We know that, the total mass is the sum of the mass of Gold and Silver, and the total volume is the sum of the volume of Gold and Silver.
9.85 = $M_{G}$ + $M_{S}$
0.675 = $V_{G}$ + $V_{S}$
2. And we can make a relation to the mass and the volume using the density.
$D_{G}$ = $\frac{M_{G}}{V_{G}}$
19.3 = $\frac{M_{G}}{V_{G}}$
$V_{G}$ = $\frac{M_{G}}{19.3}$
$D_{S}$ = $\frac{M_{S}}{V_{S}}$
10.5 = $\frac{M_{S}}{V_{S}}$
$V_{S}$ = $\frac{M_{S}}{10.5}$
3. Substitute the values of $V_{S}$ and $V_{G}$ in the second equation.
0.675 = $\frac{M_{G}}{19.3}$ + $\frac{M_{S}}{10.5}$
4. Now that we have 2 equations with 2 unknows, let's start the Algebra!
9.85 = $M_{G}$ + $M_{S}$
0.675 = $\frac{M_{G}}{19.3}$ + $\frac{M_{S}}{10.5}$
*I will use the substitution method.
$M_{S}$ = 9.85 - $M_{G}$
0.675 = $\frac{M_{G}}{19.3}$ + $\frac{9.85 - M_{G}}{10.5}$
0.675 - $\frac{9.85 - M_{G}}{10.5}$ = $\frac{M_{G}}{19.3}$
$\frac{7.0875}{10.5}$ - $\frac{9.85 - M_{G}}{10.5}$ = $\frac{M_{G}}{19.3}$
$\frac{7.0875 - 9.85 + M_{G}}{10.5}$ = $\frac{M_{G}}{19.3}$
$\frac{-2.7625 + M_{G}}{10.5}$ = $\frac{M_{G}}{19.3}$
-53.316 + 19.3$M_{G}$ = 10.5$M_{G}$
-53.316 = -8,8$M_{G}$
53.316 = 8.8$M_{G}$
$M_{G}$ = $\frac{53.316}{8.8}$
$M_{G}$ $\approx$ 6.059
5. Find the percent of Gold in mass.
Percent of Gold = $\frac{6.059}{Totalmass}$ $\times$ 100%
Percent of Gold = $\frac{6.059}{9.85}$ $\times$ 100%
Percent of Gold $\approx$ 0.6151 $\times$ 100%
Percent of Gold $\approx$ 61.51%
