document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251660>Question 251660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of two two-digit numbers is 1484. The product of their units digits is 24 and the product of their tens digits is 10. The two numbers can be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183388 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's another way to do this.<BR>\n" );
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document.write( "The product of two two-digit numbers is 1484.<BR>\n" );
document.write( " The product of their units digits is 24 and the product of their tens digits is 10.<BR>\n" );
document.write( " The two numbers can be?<BR>\n" );
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document.write( "1st two digit number 10a + b<BR>\n" );
document.write( "2nd two digit number 10c + d<BR>\n" );
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document.write( "\"The product of two two-digit numbers is 1484.\"<BR>\n" );
document.write( "(10a + b)&(10c + d) = 1484<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "100ac + 10ad + 10bc + bd<BR>\n" );
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document.write( "\"The product of their units digits is 24\"<BR>\n" );
document.write( "b * d = 24<BR>\n" );
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document.write( "\"the product of their tens digits is 10.\"<BR>\n" );
document.write( "a * c = 10<BR>\n" );
document.write( "We know that a is 5 and c is 2 or vice versa<BR>\n" );
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document.write( "In the 1st equation, we find we can replace bd with 24 and ac with 10<BR>\n" );
document.write( "100(10) + 10ad + 10bc + 24 = 1484<BR>\n" );
document.write( "1000 + 10ad + 10bc + 24 = 1484<BR>\n" );
document.write( "10ad + 10bc + 1024 = 1484<BR>\n" );
document.write( "10ad + 10bc = 1484 - 1024<BR>\n" );
document.write( "10ad + 10bc = 460<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "5ad + 5bc = 230<BR>\n" );
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document.write( "Assume a=2, c=5<BR>\n" );
document.write( "2(5d) + 5(5b) = 230<BR>\n" );
document.write( "10d + 25b = 230<BR>\n" );
document.write( "10d = 230 - 25b<BR>\n" );
document.write( "d = 23 - 2.5b<BR>\n" );
document.write( " Only two single digit integer solutions to this equation:<BR>\n" );
document.write( "b=8; d=3 (the only pair that satisfy eq: b * d = 24)<BR>\n" );
document.write( "and assuming; a=2; c=5<BR>\n" );
document.write( "therefore:<BR>\n" );
document.write( "28, 53 can be the numbers<BR>\n" );
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document.write( "check: 28 * 53 = 1484\r<BR>\n" );
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document.write( " </SPAN>\n" );
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