# 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 | High School Teacher | (Level 1) Adjunct Educator

Posted on

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 | College Teacher | (Level 2) Distinguished Educator

Posted on

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