Word problem

Question

If the value of 10 ounces of gold is d dollars and an ounce of gold is equivilant to s ounces of silver, what is the value, in dollars, of 3 ounces of silver?

Answer 1

For this problem, units are extremely important.

 

We may use the Multiplicative Identity (that is, 1) to change the units without changing the value.  This is called Dimensional Analysis.  Any value multiplied by 1 remains unchanged.

 

For this problem:    [note: choose the one so that units cancel]

   1 = (1 ounce of gold) / (s ounces of silver)  =  (s ounces of silver) / (1 ounce of gold)

   1 = (10 ounces of gold) / (d dollars)  =  (d dollars) / (10 ounces of gold) 

 

We have:

          3 ounces of silver

          (3 ounces of silver) * 1

          (3 ounces of silver) * ( (1 ounce of gold) / (s ounces of silver) )

          ( 3/s ) ounces of gold                    [ounces of silver cancel]

          ( 3/s ounces of gold ) * ( (d dollars) / (10 ounces of gold) )

           (3d)/(10s) dollars                    [ounces of gold cancel]

            (3/10)(d/s) dollars