document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6915>Question 6915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "  I really need some help with my daughters homework.  I have been away from alegbra for quite some time.  Here is her problem.\r<BR>\n" );
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document.write( "    A person has $100.00 to purchase 100 animals.  Those animals are Horses for $10.00 each, Goats for $1.00 each, and Ducks 8 for $1.00.  What formula would I use to solve this problem?  I really need your help.\r<BR>\n" );
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document.write( "   Thank you so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3792 by </B><A HREF=/tutors/aboutme.mpl?userid=glabow><B>glabow(165)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=glabow><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am surprised at your having a problem like this.<BR>\n" );
document.write( "There is not enough information to solve in closed form.<BR>\n" );
document.write( "However, you have the following information in algebraic form:<BR>\n" );
document.write( "Let x be the number of horses bought<BR>\n" );
document.write( "Let y be the number of goats bought<BR>\n" );
document.write( "Let z be the number of ducks bought\r<BR>\n" );
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document.write( "You spend 10x + y + 1/8 z = 100 dollars<BR>\n" );
document.write( "You buy x+y+z = 100 animals\r<BR>\n" );
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document.write( "So z = 100-x-y<BR>\n" );
document.write( "Replacing z with 100-x-y in the first equation gives<BR>\n" );
document.write( "10x + y + 100/8 - x/8 - y/8 = 100<BR>\n" );
document.write( "Simplifying this gives<BR>\n" );
document.write( "79x+7y=700\r<BR>\n" );
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document.write( "Since you can only buy whole animals (I assume) you are looking for integer x and y that satisfy this equation. A short table shows that<BR>\n" );
document.write( "8 horses cost 632 leaving 68 -- not divisible by 7<BR>\n" );
document.write( "7 horses cost 533 leaving 147 which equals 7 x 21<BR>\n" );
document.write( "6 horses cost 474 leaving 226 -- not divisible by 7<BR>\n" );
document.write( "5 horses cost 396 leaving 305 -- not divisible by 7<BR>\n" );
document.write( "4 horses cost 316 leaving 384 -- not divisible by 7<BR>\n" );
document.write( "3 horses cost 237 leaving 463 -- not divisible by 7<BR>\n" );
document.write( "2 horses cost 158 leaving 542 -- not divisible by 7<BR>\n" );
document.write( "1 horse costs 79 leaving 621 -- not divisible by 7<BR>\n" );
document.write( "So, x=7 and y=21 are correct.\r<BR>\n" );
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document.write( "This means you buy 72 ducks (z=100-7-21).<BR>\n" );
document.write( "Checking: 7x10 + 21 + 72/8 = 100 dollars<BR>\n" );
document.write( " </SPAN>\n" );
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