Question 0.9: Complex Unit Conversions Precious metals such as gold, silve......
Complex Unit Conversions
Precious metals such as gold, silver, and platinum are measured in troy ounces (ozt) rather than common avoirdupois ounces (oz), where 1 ozt = 31.103 g and 1 oz = 28.35 g. Furthermore, a troy pound (lbt) contains only 12 ozt while an avoirdupois pound (lb) contains 16 oz. How many ozt are in 1 lb, and how many oz are in 1 lbt? Which would you rather receive as a gift from a rich relative, 1 avoirdupois ounce of gold or 1 troy ounce? One avoirdupois pound of gold or 1 troy pound?
STRATEGY
This problem contains a lot of information that makes it sound more difficult than it is. You can cut through the difficulties, however, by setting up equations in which unwanted units cancel and only desired units remain.
One troy ounce of gold (31.103 g) is larger than one avoirdupois ounce (28.35 g) and makes a nicer gift, but one avoirdupois pound (16 oz) is much larger than one troy pound (13.17 oz) and makes a great gift.
BALLPARK CHECK
One troy ounce (31.103 g) is slightly larger than one avoirdupois ounce (28.35 g) so there will be slightly fewer of them in an avoirdupois pound, perhaps about 15 ozt/lb rather than 16 oz/lb. Furthermore, because an avoirdupois ounce is slightly smaller than a troy ounce, there will be slightly more of them in a troy pound, perhaps about 13 oz/lbt rather than 12 ozt/lbt. These estimates agree with the detailed solution.