# How do I turn this question into equations and then solve the system?  Bachelle wants to know the density of her bracelet, which is a mix of gold and silver. Density is total mass divided by...

How do I turn this question into equations and then solve the system?

Bachelle wants to know the density of her bracelet, which is a mix of gold and silver. Density is total mass divided by total volume. The density of the gold is 19.3 g/cc and the density of silver is 10.5g/cc. The jeweler told her that the volume of silver used was 10cc and the volume of gold used was 20 cc. Find the combined density of her bracelet.

mathappeal | Certified Educator

The following method does not use a system of two or three equations but rather a work/mixture approach:

Since the volume of gold is twice the volume of the silver, we can use the ratio of 2G/1S to calculate the overall density.

The d of G is 19.3g/cc and the d of S is 10.5g/cc.  So now I take 2G=2*19.3=38.6 and then add 10.5 to get a total of 49.1g/cc.

But this is 3 times the total density, because we added the densities of two golds and one silver.  So, dividing 49.1 by 3, we get 16.36666... or, rounding to two decimal places, 16.37 g/cc.

Make sure not to confuse mass and weight.  Weight takes into account the force of gravity; mass does not.

justaguide | Certified Educator

The volume of silver used in Bachelle's bracelet is 10cc and the volume of gold used is 20 cc.

As the density of gold is 19.3 g/cc, the weight of gold used in her bracelet is 19.3*20 = 386 g. As the density of silver is 10.5 g/cc, the weight of silver used in her bracelet is 10.5*10 = 105 g.

The total weight of her bracelet is 105 + 386 = 491 g

The volume of her bracelet is 10 + 20 = 30 cc

This allows us to find the density using the formula: density = mass/volume. The density of the bracelet is 491/30 = 16.36 g/cc

The combined density of her bracelet is 16.36 g/cc