7. You are given 1000 equal sized gem stones with a total mass of exactly 3 g. T

Question

7. You are given 1000 equal sized gem stones with a total mass of exactly 3 g. These gems are valued at $1000 per oz. (Note: 1.00 oz = 28.35 g) Answer the following using unit – factor analysis.

a. How much money are you out if you lose 50 stones?

b. If you now receive an additional handful of these gems, how would you determine the value of this handful by weighing? Tell exactly how you would go about it.

c. Could you determine the value of this handful by a counting procedure? What assumption would the counting procedure depend upon?

Explanation / Answer

a)100 stones weigh = 3 gm

50 gms weigh =3*50/100= 1.5 gms

28.35 gm weigh $1000

1.5 gms weigh 1.5*$1000/28.35=$52.63 amount lost

b) since 28.35 gms correspond to 1 oz, weigh the gem and from mass convert them into OZ. Since cost per OZ is known, its value can be determined.

c) assume all the gems are of equal mass. since 100 gems give 3 gms counting the gems also helps.

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