Question

. 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?

Answer 1

Solution :-

a). Lets convert the 3 g to oz

3g * 1 oz / 28.35 g = 0.10582 oz

So now lets calculate the mass of 50 gems

(50 gem * 3g / 1000 gem)*(1 oz / 28.35 g) = 0.005291 oz

So value of 0.10582 oz * $1000 / 1 oz = $ 105.82

So lets calculate the value of the 0.005291 oz

0.005291 oz * $105.82 / 0.10582 oz = $ 5.291

So the you are out of $ 5.291

b) the value of the hadful of gems can be calculated using the weighing them because as we know 1000 gem weighs 3 g has value of $105.82

so by weighing the hadful gems we can find their mass and using that mass we can calculate their value

(mass of haldful gem * $105.82 / 3 g) = $ value of handful gems

c) we can determine the value of the handful gems by couting but the assumption that we need to make is all of them have same mass and size.