document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328686>Question 328686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ann needs 6 pens and 14 books costing a total of Sh. 310. Agnes, Annes sister  needs 12 similar pens and 10 similar books which cost a total of Sh. 314. How much should their mother have to buy all the books? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235474 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ann needs 6 pens and 14 books costing a total of Sh. 310.<BR>\n" );
document.write( "Agnes needs 12 pens and 10 books which cost a total of Sh. 314.\r<BR>\n" );
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document.write( "Apparently the pens cost the same each and the books cost the same each.\r<BR>\n" );
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document.write( "You have 2 equations that need to be solved simultaneously\r<BR>\n" );
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document.write( "Let p = price of each pen<BR>\n" );
document.write( "Let b = price of each book\r<BR>\n" );
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document.write( "Your equations are:\r<BR>\n" );
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document.write( "6p + 14b = 310<BR>\n" );
document.write( "12p + 10b = 314\r<BR>\n" );
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document.write( "If we multiply both sides of the first equation by 2, then we can cancel out the p and solve for b.   multiplying both sides of any equation by the same number does not change the equality.  If it was equal before, it will be equal after.\r<BR>\n" );
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document.write( "Multiply both sides of the first equation to get:\r<BR>\n" );
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document.write( "12p + 28b = 620\r<BR>\n" );
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document.write( "subtract the second equation from that to get:\r<BR>\n" );
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document.write( "12p + 28b = 620<BR>\n" );
document.write( "minus:<BR>\n" );
document.write( "12p + 10b = 314<BR>\n" );
document.write( "equals:<BR>\n" );
document.write( "0p + 18b = 306<BR>\n" );
document.write( "which is equivalent to:<BR>\n" );
document.write( "18b = 306\r<BR>\n" );
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document.write( "divide both sides of this equation by 18 to get:\r<BR>\n" );
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document.write( "b = 17\r<BR>\n" );
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document.write( "the price of each book is Sh. 17.\r<BR>\n" );
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document.write( "Since you know that each book costs Sh. 17, you can solve for the price of each pen by substituting in one of the original equations.\r<BR>\n" );
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document.write( "Take 6p + 14b = 310\r<BR>\n" );
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document.write( "When b = 17, this equation becomes:\r<BR>\n" );
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document.write( "6p + 238 = 310\r<BR>\n" );
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document.write( "subtract 238 from both sides of this equation to get:\r<BR>\n" );
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document.write( "6p = 72\r<BR>\n" );
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document.write( "divide both sides of this equation by 6 to get:\r<BR>\n" );
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document.write( "p = 12\r<BR>\n" );
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document.write( "the price of each pen is Sh. 12 and the price of each book is Sh. 17.\r<BR>\n" );
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document.write( "From your original equations, you can see that:\r<BR>\n" );
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document.write( "6p + 14b = 310<BR>\n" );
document.write( "12p + 10b = 314\r<BR>\n" );
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document.write( "gets you a total of:\r<BR>\n" );
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document.write( "18 pens and 24 books for a total of Sh. 624.\r<BR>\n" );
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document.write( "multiply the number of pens by the price of each pen and the number of each book by the price of each book to get:\r<BR>\n" );
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document.write( "18 * 12 = 216 total cost for pens<BR>\n" );
document.write( "24 * 17 = 408 total cost for books\r<BR>\n" );
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document.write( "total spent is 216 + 408 = 624 which agrees with the total you got just above.\r<BR>\n" );
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document.write( "Your answer is that the amount of money spent on books is equal to Sh. 408\r<BR>\n" );
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document.write( " </SPAN>\n" );
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