This is a problem of proportions and average density. You can find the density of both metals online:

Density of Copper: 8.94 g/cm^3

Density of Lead: 11.34 g/cm^3

The easiest way to do this is to say x is the proportion of the copper spheres out of the total number...

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This is a problem of proportions and average density. You can find the density of both metals online:

Density of Copper: 8.94 g/cm^3

Density of Lead: 11.34 g/cm^3

The easiest way to do this is to say x is the proportion of the copper spheres out of the total number of spheres, making the fraction of lead spheres equal to 1-x (because we only have lead and copper spheres).

This would make the average density the following (in g/cm^3):

8.94x + 11.34(1 - x)

To get total mass, we simply multiply the volume the spheres take up by their average density:

m = dv

From the problem and our expression for average density, we get the following equation (keep in mind mass needs to be in grams):

4360 = (8.94x + 11.34(1 - x))*427

Simplifying the right side:

4360 = 427(8.94x + 11.34 - 11.34x)

4360 = 427(-2.4x + 11.34)

4360 = -1024.8x + 4842.18

Now, we can solve for x, first by subtracting, then by dividing:

-482.18 = -1024.8x

**0.471 = x**

Notice our calculated fraction of copper spheres has 3 significant figures, like every number given in the problem.

Because they ask for a *percent* of copper spheres, you just multiply x by 100% and get the following:

Percent of copper spheres = **47.1%**