Precious metals and gems are measured in troy weights in the english system: 24 grains = 1 pennyweight (exact) 20 pennyweight = 1 troy ounce (exact) 12 troy ounces = 1 troy pound (exact) 1 grain = 0.0648 g 1 carat = 0.200 g a. the most common english unit of math is the pound avoirdupois. what is 1 troy pound in kilograms and in pounds? b. what is the mass of a troy ounce of gold in gram and in carats? c. the density of gold is 19.3 g/cm 3 . what is the volume of a troy pound of gold?

Given that

24 grains = 1 pennyweight (exact)

20 pennyweight = 1 troy ounce (exact)

12 troy ounces = 1 troy pound (exact)

1 grain = 0.0648 g

1 carat = 0.200 g

a)  Mass of one troy pound in Kg and pounds

(i) in kilograms

1 troy pound = 12 troy ounces

                     = 1 2X 20 penny weight

                      = 12 X 20 X 24 grains

                      = 12 X 20 X 24 X 0.0648 grams

                    = 373.248 g

                    =0.37325 Kg

ii) in pounds

1 gram = 0.002205 pounds

373.248 g = 0.823 pounds

b) 1 troy ounce = 20 penny weight

                        =  20 X 24 grains

                      = 20 X 24 X 0.0648 g

                   = 31.104 g

one carat = 0.20 g

so 31.104g = 31.104 / 0.2 carot = 155.52 carat

c) density of gold is 19.3 g/cm 3

volume of 1 troy pound

Mass of 1 troy pound in grams = 373. 248 g

Volume  = mass / density = 373.248 / 19.3  = 19.34 cm^3