Question

An 18 karat gold bracelet has a mass of 56.18 g. 1 troy ounce of pure gold is 31.03 g. What is the value of the bracelet in US dollars?

Answer 1

Your bracelet is worth $1692.00.

Given: 1 ozt = 31.103 g

From this equality, there are two conversion factors:

`(1 "ozt")/(31.03 "g")` and `(31.03 "g")/(1 "ozt")`.

These conversion factors are equal to each other and to 1.

Convert the mass in grams to troy ounces (ozt).

Multiply 56.18 g × the conversion factor between troy ounces and grams, in which grams are on the bottom and troy ounces are on the top. This will cancel the grams and leave you with troy ounces.

`"56.18 g" × "1 ozt"/"31.103 g" = "1.806 ozt"`

But pure gold is 24 kt. Your bracelet is only 18 kt gold.

The mass of pure gold in it is

`"1.806 ozt"× "18 kt"/"24 kt" = "1.355 ozt"`

Now you need to multiply 1.355 ozt × the cost per troy ounce of pure gold.

`"1.355 ozt" × "$1249.00"/"1 ozt" = "$1692"`