Profit & Loss

Question

Sam sold his car to David at a profit of 10%. David sold the car to Rita for $209 at a loss of 5%. How much did the car cost Sam?

Answer 1

Read and re-read the problem until you understand it and can put it into your own words.  How’s this:  Starting with x, 10% increase, then 5% decrease is $209.

 

Let x = price Sam paid

 

Translate:

   "Sam sold his car to David at a profit of 10%"     

          means Sam sold car for 1.10x

  "David sold the car to Rita for $209 at a loss of 5%"    means

                                             $209 = 0.95(1.10x)

 

   $209 = 0.95(1.10x)             [re-write]

     $200 = x

   

Checking (very important):

 

Sam sold his $200 car to David at a profit of 10% ($220).  David sold the car to Rita for $209, which is a loss of $11 or $11/$220 or 5%).     Check!