document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=49185>Question 49185</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "My daughter has not received her book yet. This is 7th grade prealgebra. A word problem was written on the board as follows:<BR>\n" );
document.write( "3 ducks and 2 ducklings weight 32 ounces, 4 ducks and 3 ducklins weigh 44 ounces. All the ducks weigh the same and all ducklings weigh the same. What would 2 ducks and 1 duckling weigh?  He gave the following answer which we can not understand: (3D+2d=32)3=9D+6d=96; (4D+3d=44)-2=(-8D+-6d)=-88; 3(8)+2d=32, 24+2d=32, 24+2d-24=32-24, 2d=8, 2d*8=16d, 16d, d =4+16=20. Please help<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 #32622 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=32622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let D = the weight of 1 Duck.<BR>\n" );
document.write( "Let d = the weight of 1 duckling.<BR>\n" );
document.write( "From the problem description, you can write a system of equations.\r<BR>\n" );
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document.write( "1) 3D + 2d = 32  (3 Ducks (D) and (+) 2 ducklings (d) weigh 32 ounces.)<BR>\n" );
document.write( "2) 4D + 3d = 44  (4 Ducks (D) and (+) 3 ducklings (d) weigh 44 ounces.)\r<BR>\n" );
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document.write( "To solve this system of equations, multiply equation 1) by 3 and equation 2) by -2, then add the two equations.\r<BR>\n" );
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document.write( "1a)  3(3D + 2d = 32) -> 1b) 9D + 6d = 96<BR>\n" );
document.write( "2a) -2(4D + 3d = 44) -> 2b) -8D - 6d = -88  Add these two equations, 1b)+2b).<BR>\n" );
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document.write( "........................D = 8  One Duck weighs 8 ounces. Now substitute this into equation 1) and solve for d.\r<BR>\n" );
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document.write( "1) 3(8) + 2d = 32<BR>\n" );
document.write( "24 + 2d = 32  Subtract 24 from both sides of the equation.<BR>\n" );
document.write( "2d = 8 Divide both sides by 2.<BR>\n" );
document.write( "d = 4  One duckling weighs 4 ounces. \r<BR>\n" );
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document.write( "Finally, 2 Ducks and 1 duckling = 2D + 1d = 2(8) + 1(4) = 16 + 4 = 20 ounces. </SPAN>\n" );
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