SOLUTION: Grace sells two sets of commemorative coins for $750 each. She gains 25% on one and lose 25% on the other. Find the overall profit or loss percent

Grace sells it for $750 and gains 25%.                                                           (1)


Let X be the price she BOUGHT  this coin some time ago.


Then the statement (1) means that she sold for the greater price, and

    750 - X = 0.25*X,   or  750 = 0.25*X + X = 1.25X;  hence  X =  = 600.


Thus Grace bought this coin for $600 and sold for $750, making profit of  $750 - $600 = $150.    (2)

Grace sells it for $750 and lose 25%.                                                            (3)


Let Y be the price she BOUGHT  this coin some time ago.


Then the statement (1) means that she sold for the lesser price, and

    Y - 750 = 0.25*Y,   or  750 = Y - 0.25*Y = 0.75*Y;  hence  Y =  = 1000.


Thus Grace bought this coin for $1000 and sold for $750, losing $1000 - $750 = $250.             (4)



Hence, from (2) and (4), she gained $150 with first coin and lose $250 with second coin.


Overall, she lose  $250 - $150 = $100.


To find overall loss percent, we should relate these $100 to the sum  X + Y = $600 + $1000 = $1600.


Thus overall lose percent is   =  = 6.25%.     ANSWER