document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=938682>Question 938682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One type of candy sells for $2 per pound and another type sells for $3 per pound. An order for 18 pounds costs $47. How much of each type of candy was purchased?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #571866 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=571866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "Type A candy = $2 / lb<BR>\n" );
document.write( "Type B candy = $3 / lb<BR>\n" );
document.write( "18 pounds total cost $47.<BR>\n" );
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document.write( "Solution method 1: using system of two equations,<BR>\n" );
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document.write( "A,B = respective weight of each candy purchased in pounds.<BR>\n" );
document.write( "A+B=18....(1)<BR>\n" );
document.write( "2A+3B=47....(2)<BR>\n" );
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document.write( "Solve by substitution<BR>\n" );
document.write( "A=18-B....(1a)<BR>\n" );
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document.write( "substitute (1a) in (2)<BR>\n" );
document.write( "2(18-B)+3B=47....(3)<BR>\n" );
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document.write( "Solve for B<BR>\n" );
document.write( "36-2B+3B=47<BR>\n" );
document.write( "B=47-36=11....(4)<BR>\n" );
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document.write( "substitute (4) into (1a)<BR>\n" );
document.write( "A=18-B=18-11=7<BR>\n" );
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document.write( "Answer: 7 lbs of A and 11 lbs of B were purchased.<BR>\n" );
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document.write( "Check: 7*2+11*3=$47, ok.<BR>\n" );
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document.write( "Method 2: mental reasoning<BR>\n" );
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document.write( "Given:<BR>\n" );
document.write( "Type A candy = $2 / lb<BR>\n" );
document.write( "Type B candy = $3 / lb<BR>\n" );
document.write( "18 pounds total cost $47.\r<BR>\n" );
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document.write( "step 1: If all 18 lbs were type A, it would have cost $2*18=$36<BR>\n" );
document.write( "step 2: There is an excess cost of $47-$36 = $11, <BR>\n" );
document.write( "        so number of pounds of type B purchased = $11/($3-$2)=11 lbs<BR>\n" );
document.write( "step 3: weight of type A purchased = 18-11=7 lbs.<BR>\n" );
document.write( "Answer: 7 lbs of A and 11 lbs of B. </SPAN>\n" );
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