document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199747>Question 1199747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Raj spent 25% of his money on clothes and 1/3 of the remainder on food. After giving $441 to his parents, he was left with 41% of his original sum of money. How much money did he have at first? </SPAN>\n" );
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document.write( "x = the amount of money, in dollars, Raj starts with\r<BR>\n" );
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document.write( "25% = 0.25<BR>\n" );
document.write( "25% of x = 0.25x<BR>\n" );
document.write( "Raj spent 0.25x dollars on clothes.<BR>\n" );
document.write( "He has 0.75x dollars left, ie 75% of his money remains.\r<BR>\n" );
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document.write( "1/3 of the remainder = (1/3)*(0.75x)<BR>\n" );
document.write( "1/3 of the remainder = (1/3)*((3/4)x)<BR>\n" );
document.write( "1/3 of the remainder = (1/4)x<BR>\n" );
document.write( "1/3 of the remainder = 0.25x<BR>\n" );
document.write( "Raj spent 0.25x dollars on food.\r<BR>\n" );
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document.write( "Total amount spent = 0.25x+0.25x = 0.50x<BR>\n" );
document.write( "He spent 50%, aka half, of his money on clothes and food combined.\r<BR>\n" );
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document.write( "Now subtract off $441 that he gives to his parents.<BR>\n" );
document.write( "Raj now has 0.50x-441 dollars.\r<BR>\n" );
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document.write( "Set this equal to 0.41x to reflect the idea he has 41% of his original money.<BR>\n" );
document.write( "Solve for x.\r<BR>\n" );
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document.write( "0.50x-441 = 0.41x<BR>\n" );
document.write( "0.50x = 0.41x+441<BR>\n" );
document.write( "0.50x-0.41x=441<BR>\n" );
document.write( "0.09x=441<BR>\n" );
document.write( "x=441/0.09<BR>\n" );
document.write( "x=<font color=red size=4>4900</font>\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "25% of $4900 = 0.25*4900 = 1225<BR>\n" );
document.write( "Raj spent $1225 on clothes.\r<BR>\n" );
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document.write( "Remainder after buying clothes = 4900 - 1225 = 3675\r<BR>\n" );
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document.write( "1/3 of remainder = (1/3)*(3675) = 1225<BR>\n" );
document.write( "Raj spent $1225 on food.\r<BR>\n" );
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document.write( "total spent = clothes+food = 1225+1225 = 2450 dollars.\r<BR>\n" );
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document.write( "Now he hands over $441<BR>\n" );
document.write( "2450-441 = 2009<BR>\n" );
document.write( "Raj is left with $2009\r<BR>\n" );
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document.write( "Divide this over the original amount (4900)<BR>\n" );
document.write( "2009/4900 = 0.41<BR>\n" );
document.write( "this shows Raj has 41% of his original money at this point. <BR>\n" );
document.write( "The answer is confirmed.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>$4900</font><BR>\n" );
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