document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124380>Question 1124380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, please help me solve this question:\r<BR>\n" );
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document.write( "SCRAP is a 5-digit number. The digits S,C,R,A, and P are used in these addition problems: A+A+A=CA and RS+RS+RS= PR\r<BR>\n" );
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document.write( "What number is scrap? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740716 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=740716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "In order to solve this, one has to assume that two different letters cannot stand for the same digit.\r<BR>\n" );
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document.write( "Given that, we first look at A + A + A = CA, which is to say 3*A = CA.\r<BR>\n" );
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document.write( "Since the result is a two digit number, A must be larger than 3 because 3 times 3 is only 9.  Also, A must be 9 or smaller because 9 is the largest single digit.  Then looking at a multiplication table in the 3s column where the multiplier is 4 or larger, the only result where the second digit is the same as the multiplier is 3 X 5 = 15.  Therefore A is 5 and C is 1.\r<BR>\n" );
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document.write( "Since 3 times RS is also a 2 digit number with two different digits, RS must be 32 or less because it can't be 33 and anything larger would have a result of three digits, and the smallest 2 digit number is 10 so it must be at least that.  We want to find a multiple of 3 where the tens digit of the multiplier is the same as the ones digit of the product.\r<BR>\n" );
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document.write( "For multipliers with 1 as a tens digit, the only multiplier that qualifies is 17:  3 X 17 = 51.  For multipliers with 2 as a tens digit, the only multiplier that qualifies is 24:  3 X 24 = 72.  And for multipliers with 3 as a tens digit, the qualifier is 31:  3 X 31 = 93.\r<BR>\n" );
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document.write( "But we have already identified C = 1, so 17 and 31 are disqualified, so RS is 24 and PR is 72.\r<BR>\n" );
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document.write( "SCRAP = 41257<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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