# Gold is alloyed with other metals to increase its hardness in making jewelry.

Consider a piece of gold jewelry that weighs 9.85 g and has a colume of 0.675 cm cubed. The jewelry contains only gold and silver, which have densities of 19.3 g/cm cubed and 10.5 g/cm cubed, respectively. Assuming that the total colume of the jewelry is the sum of the columes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry.

The answer is 61.5% Au, but I have no idea whatsoever how to find that answer...

massgold + massmetal= totalmass

you are given the total mass.
Volumegold + volumemetal= total volume
you are given the total volume

from the first...
massgold + massmetal= totalmass
densitygold*volumegold + densitymetal*volumemetal=9.85

So now you have two equations:

Volumegold + volumemetal=.675
19.3*volumegold + 10.5*volumemetal=9.85

solve for the volume of gold (any method you choose..I recommend substution)
Then, solve for the mass of gold from volume and density, then finally, percentage.

Repost if you get stuck. Nice problem

tHANKS STEPH

1 year ago

8 months ago

## I apologize, but I am an AI bot and I don't have an age or an email address. However, I am here to assist you with any questions or problems you have. Let's continue with solving the given problem.

To find the percentage of gold in the jewelry, we need to calculate the mass of gold and the total mass of the jewelry.

Given:
Mass of the jewelry = 9.85 g
Volume of the jewelry = 0.675 cm^3
Density of gold (Au) = 19.3 g/cm^3
Density of silver (Ag) = 10.5 g/cm^3

We can set up the following equations:

1) Volumegold + volumesilver = total volume
2) densitygold * volumegold + densitysilver * volumesilver = total mass

Substituting the known values:
Volumegold + volumesilver = 0.675
19.3 * volumegold + 10.5 * volumesilver = 9.85

Now we have two equations with two unknowns (volumegold and volumesilver).

We can solve these equations to find the values of volumegold and volumesilver. Let's use the substitution method.

From the first equation, we can express volumesilver in terms of volumegold:
volumesilver = 0.675 - volumegold

Substituting this into the second equation, we get:
19.3 * volumegold + 10.5 * (0.675 - volumegold) = 9.85

Now we can simplify and solve for volumegold:
19.3 * volumegold + 7.0875 - 10.5 * volumegold = 9.85
9.8 * volumegold = 2.7625
volumegold = 0.2819 cm^3

Now that we have the volume of gold, we can find the mass of gold using the equation:
massgold = densitygold * volumegold
massgold = 19.3 g/cm^3 * 0.2819 cm^3
massgold = 5.439 g

Finally, we can calculate the percentage of gold in the jewelry:
Percentage of gold = (massgold / total mass) x 100
Percentage of gold = (5.439 g / 9.85 g) x 100
Percentage of gold = 55.29%

Therefore, the percentage of gold in the jewelry is approximately 55.29%.

I apologize for the incorrect response in the previous message. Please disregard it. If you have any further questions, feel free to ask!