document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208259>Question 1208259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "In a box there were some 50c coins and half as many 20cent coins. When 40 50c and 8 20cent coins were added.the value in the box would be 4 times as much as it was before.<BR>\n" );
document.write( "What is the total value at first<BR>\n" );
document.write( "What is the total of coins at the end.<BR>\n" );
document.write( "This is word for word from textbook.  </SPAN>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "total value at first = <font color=red>720 cents</font> = <font color=red>$7.20</font><BR>\n" );
document.write( "total number of coins at the end = <font color=red>66 coins</font><BR>\n" );
document.write( "Extras: started with 6 coins worth 20cents each, and 12 coins worth 50cents each.\r<BR>\n" );
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document.write( "Work Shown\r<BR>\n" );
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document.write( "x = starting number of 20cent coins<BR>\n" );
document.write( "2x = starting number of 50cent coins<BR>\n" );
document.write( "Note that x is half of 2x.\r<BR>\n" );
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document.write( "A = 20x = starting value of just the 20cent coins<BR>\n" );
document.write( "B = 50*(2x) = 100x = starting value of just the 50cent coins<BR>\n" );
document.write( "C = A+B = 20x+100x = 120x = value of original group of coins (before any extras are added). Values are in cents.\r<BR>\n" );
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document.write( "Now add 8 copies of a 20cent coin and 40 copies of the 50cent coin.<BR>\n" );
document.write( "x bumps up to x+8 to represent the new number of 20cent coins.<BR>\n" );
document.write( "2x bumps up to 2x+40 to represent the new number of 50cent coins.<BR>\n" );
document.write( "D = 20*(x+8) = 20x+160 = new value of just the 20cent coins<BR>\n" );
document.write( "E = 50*(2x+40) = 100x+2000 = new value of just the 50cent coins<BR>\n" );
document.write( "F = D+E = (20x+160)+(100x+2000) = 120x+2160 = new total value in cents.\r<BR>\n" );
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document.write( "The new value (F) is 4 times as much as before (C)<BR>\n" );
document.write( "new = 4*old<BR>\n" );
document.write( "F = 4*C<BR>\n" );
document.write( "120x+2160 = 4(120x)<BR>\n" );
document.write( "120x+2160 = 480x<BR>\n" );
document.write( "2160 = 480x-120x<BR>\n" );
document.write( "2160 = 360x<BR>\n" );
document.write( "x = 2160/360<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "There are 6 coins worth 20 cents each in the box at first.<BR>\n" );
document.write( "There are also 12 coins worth 50 cents each in the box at first (since 2x = 2*6 = 12)<BR>\n" );
document.write( "C = total starting value = 6*20+12*50 = <font color=red>720 cents</font> = <font color=red>$7.20</font>\r<BR>\n" );
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document.write( "Now add 8 copies of a 20cent coin and 40 copies of the 50cent coin.<BR>\n" );
document.write( "6+8 = 14 copies of a 20cent coin <BR>\n" );
document.write( "12+40 = 52 copies of a 50cent coin<BR>\n" );
document.write( "The box now has 14+52 = <font color=red>66 coins</font><BR>\n" );
document.write( "F = new total value = 14*20+52*50 = 2880 cents = $28.80\r<BR>\n" );
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document.write( "The jump from C = 720 cents to F = 2880 cents is \"times 4\" since 720*4 = 2880<BR>\n" );
document.write( "Or you could note that F/C = 2880/720 = 4.<BR>\n" );
document.write( "We have confirmed the answers are correct.\r<BR>\n" );
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document.write( "If you only cared about the total value, and not the coin counts, then you can follow this method:\r<BR>\n" );
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document.write( "m = total value of the original group of coins (before any extras added)<BR>\n" );
document.write( "value in cents\r<BR>\n" );
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document.write( "Adding 40 coins worth 50cents each and 8 coins worth 20cents each will give an additional 40*50+8*20 = 2160 cents<BR>\n" );
document.write( "m bumps up to m+2160 which represents the new total value.<BR>\n" );
document.write( "This expression is 4 times that of the original value.\r<BR>\n" );
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document.write( "new = 4*old<BR>\n" );
document.write( "m+2160 = 4m<BR>\n" );
document.write( "4m-m = 2160<BR>\n" );
document.write( "3m = 2160<BR>\n" );
document.write( "m = 2160/3<BR>\n" );
document.write( "m = <font color=red>720 cents</font> is the starting total value<BR>\n" );
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