Question 1174085
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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
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<B>Solution</B>



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Consider first coin.</U>



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


Let X be the price she <U>BOUGHT</U>  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 = {{{750/1.25}}} = 600.


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



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Next consider second coin.</U>



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


Let Y be the price she <U>BOUGHT</U>  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 = {{{750/0.75}}} = 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  {{{(100/1600)*100}}} = {{{(1/16)*100}}} = 6.25%.     <U>ANSWER</U>
</pre>

Solved.


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It is a nice entertainment problem.


It contains a &nbsp;HUGE &nbsp;underwater stone, &nbsp;and in order to solve the problem successfully, you should 
discover this underwater stone first.


Even after this discovering, &nbsp;still remains and there is a challenge to make the overall analysis accurately.


But it looks like I was able to do everything correctly &nbsp;(I hope).



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After reading my solution, &nbsp;do not forget to post your &nbsp;THANKS &nbsp;to me for my teaching.