document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205102>Question 1205102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eli Al’s has a collection of marbles. If he gives away 3/5 of his marbles to his friend and then buys 20 more marbles, he will have 100 marbles in total. How many marbles did Eli Al have originally? </SPAN>\n" );
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document.write( "x = number of marbles he started with<BR>\n" );
document.write( "(3/5)x = number of marbles given away<BR>\n" );
document.write( "(2/5)x = number of marbles he keeps<BR>\n" );
document.write( "(2/5)x+20 = amount after buying 20 more marbles\r<BR>\n" );
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document.write( "(2/5)x+20 = 100<BR>\n" );
document.write( "(2/5)x = 100-20<BR>\n" );
document.write( "(2/5)x = 80<BR>\n" );
document.write( "x = 80*(5/2)<BR>\n" );
document.write( "x = <font color=red size=4>200</font>\r<BR>\n" );
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document.write( "Another way to solve<BR>\n" );
document.write( "(2/5)x+20 = 100<BR>\n" );
document.write( "5*( (2/5)x+20 ) = 5*100<BR>\n" );
document.write( "5*(2/5)x + 5*20 = 500<BR>\n" );
document.write( "2x + 100 = 500<BR>\n" );
document.write( "2x = 500 - 100<BR>\n" );
document.write( "2x = 400<BR>\n" );
document.write( "x = 400/2<BR>\n" );
document.write( "x = <font color=red size=4>200</font>\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "He started with <font color=red>200</font> marbles.<BR>\n" );
document.write( "3/5 of which is (3/5)*200 = 0.6*200 = 120<BR>\n" );
document.write( "He gives away 120 marbles and keeps 200-120 = 80. Note how (2/5)*200 = 0.4*200 = 80.<BR>\n" );
document.write( "Then he buys 20 marbles to get 80+20 = 100 total at the end. We have confirmed the answer.\r<BR>\n" );
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document.write( "Another way to check:<BR>\n" );
document.write( "(2/5)x+20 = 100<BR>\n" );
document.write( "(2/5)*<font color=red>200</font>+20 = 100<BR>\n" );
document.write( "0.4*200+20 = 100<BR>\n" );
document.write( "80+20 = 100<BR>\n" );
document.write( "100 = 100<BR>\n" );
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