Question

Gold is alloyed (mixed) with other metals to increase its hardness in making jewelry.

Answer 1

Answer:

A) 54.04%

B) 13-karat

Explanation:

A) From the problem we have

1) Mg + Ms = 9.40 g

2) Vg + Vs = 0.675 cm³

Where M stands for mass, V stands for volume, and g and s stand for gold and silver respectively.

We can rewrite the first equation using the density values:

3) Vg * 19.3 g/cm³ + Vs * 10.5 g/cm³ = 9.40

So now we have a system of two equations (2 and 3) with two unknowns:

We express Vg in terms of Vs:

• Vg + Vs = 0.675 cm³

• Vg = 0.675 - Vs

We replace the value of Vg in equation 3:

• Vg * 19.3 + Vs * 10.5 = 9.40

• (0.675-Vs) * 19.3 + Vs * 10.5 = 9.40

• 13.0275 - 19.3Vs + 10.5Vs = 9.40

• -8.8 Vs + 13.0275 = 9.40

• Vs = 0.412 cm³

Now we calculate Vg:

• Vg + Vs = 0.675 cm³

• Vg + 0.412 cm³ = 0.675 cm³

• Vg = 0.263 cm³

We calculate Mg from Vg:

• 0.263 cm³ * 19.3 g/cm³ = 5.08 g

We calculate the mass percentage of gold:

• 5.08 / 9.40 * 100% = 54.04%

B)

We multiply 24 by the percentage fraction:

• 24 * 54.04/100 = 12.97-karat ≅ 13-karat