document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173505>Question 1173505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Samy counts his change.  He has twice as many 10 ¢ coins as he has 5 ¢ and 6 25 ¢ coins more than 10 ¢.  He also has 4 $ 1 coins and 7 $ 2 coins.  In all, he has $ 29.25.<BR>\n" );
document.write( " How many of each of Samy's pieces does he have? </SPAN>\n" );
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document.write( "let x be the number of 5 cent coins<BR>\n" );
document.write( "then 2x is the number of 10 cent coins  (twice as many as 5 cent)<BR>\n" );
document.write( "then 2x+6 is the number of 25 cent coins  (6 more than the number of 10 cent)<br><BR>\n" );
document.write( "The total value of the coins, including 4 $1 coins and 7 $2 coins, is $29.25:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%29%2B10%282x%29%2B25%282x%2B6%29%2B4%28100%29%2B7%28200%29+=+2925 ALIGN=MIDDLE  ALT=\"5%28x%29%2B10%282x%29%2B25%282x%2B6%29%2B4%28100%29%2B7%28200%29+=+2925\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B20x%2B50x%2B150%2B400%2B1400+=+2925 ALIGN=MIDDLE  ALT=\"5x%2B20x%2B50x%2B150%2B400%2B1400+=+2925\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75x%2B1950+=+2925 ALIGN=MIDDLE  ALT=\"75x%2B1950+=+2925\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75x+=+975 ALIGN=MIDDLE  ALT=\"75x+=+975\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13 ALIGN=MIDDLE  ALT=\"x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "5 cent coins: x = 13<BR>\n" );
document.write( "10 cent coins: 2x = 26<BR>\n" );
document.write( "25 cent coins: 2x+6 = 32<br><BR>\n" );
document.write( "CHECK: 13(5)+26(10)+32(25)+4(100)+7(200) = 65+260+800+400+1400 = 2925<br><BR>\n" );
document.write( "A solution using logical reasoning can follow nearly the same path of calculations.<br><BR>\n" );
document.write( "(1) Count the 4 $1 coins and the 7 $2 coins first.  That is $18, leaving $11.25.<BR>\n" );
document.write( "(2) Count the \"extra\" 6 quarters next; that is $1.50, leaving $9.75.<BR>\n" );
document.write( "(3) What is left is x 5 cent coins, 2x 10 cent coins, and 2x quarters.  Group those coins into groups of 1 5 cent coin, 2 10 cent coins, and 2 25 cent coins.<BR>\n" );
document.write( "(4) The value of each of those groups is 5+20+50 = 75 cents. The number of groups, at 75 cents each, needed to make the remaining $9.75 is 975/75 = 13.<br><BR>\n" );
document.write( "So there are 13 5 cent coins, 2*13=26 10 cent coins, and 2*13+6=32 25 cent coins.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );