document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170623>Question 1170623</A>: <I><SPAN STYLE=\"word-break: break-all;\">  What is the answer to A shipment from a toy factory has a total of 65 unicycles, bicycles, and skateboards combined. The shipment had 160 total wheels. The number of bicycles wheels was the same as the number of skateboard wheels. Create and solve a system of equations to find how many each type of toy was in the shipment. Also I need to show my work.<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 #795472 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=795472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> u = number of unicycles<BR>\n" );
document.write( "b = number of bicycles<BR>\n" );
document.write( "s = number of skateboards.\r<BR>\n" );
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document.write( "u + b + s = 65\r<BR>\n" );
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document.write( "the shipment had a total of 160 wheels.<BR>\n" );
document.write( "the number of bicycle wheels was the same as the number of skateboard wheels.\r<BR>\n" );
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document.write( "the number of wheels per unicycle = 1.<BR>\n" );
document.write( "the number of wheels per bicycle = 2<BR>\n" );
document.write( "the number of wheels per skateboard = 4\r<BR>\n" );
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document.write( "the equation for this is:\r<BR>\n" );
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document.write( "u + 2 * b + 4 * s = 160\r<BR>\n" );
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document.write( "you are given that the number of bicycle wheels was the same as the number of skateboard wheels.\r<BR>\n" );
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document.write( "the equation for this is:\r<BR>\n" );
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document.write( "2 * b = 4 * s\r<BR>\n" );
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document.write( "you have 3 equations that needs to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "u + b + s = 65<BR>\n" );
document.write( "u + 2 * b + 4 * s = 160<BR>\n" );
document.write( "2 * b = 4 * s\r<BR>\n" );
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document.write( "in the equation of 2 * b = 4 * s, solve for b to get:\r<BR>\n" );
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document.write( "b = 2 * s\r<BR>\n" );
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document.write( "replace b with 2 * s in the other 2 equations to get:\r<BR>\n" );
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document.write( "u + 2 * s + s = 65<BR>\n" );
document.write( "u + 2 * (2 * s) + 4 * s = 160\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "u + 3 * s = 65<BR>\n" );
document.write( "u + 8 * s = 160\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "5 * s = 95\r<BR>\n" );
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document.write( "solve for s to get:\r<BR>\n" );
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document.write( "s = 19\r<BR>\n" );
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document.write( "since b = 2 * s, then b = 38\r<BR>\n" );
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document.write( "in the equation of u + b + s = 65, replace b with 38 and s with 19 to get:\r<BR>\n" );
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document.write( "u + 38 + 19 = 65\r<BR>\n" );
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document.write( "solve for u to get:\r<BR>\n" );
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document.write( "u = 65 - 38 - 19 = 8\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "number of unicycles = 8<BR>\n" );
document.write( "number of bicycles = 38<BR>\n" );
document.write( "number of skateboards = 19\r<BR>\n" );
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document.write( "confirm your solution by replacing u and b and s with those numbers in both original equations to get:\r<BR>\n" );
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document.write( "u + b + s = 65 becomes 8 + 38 + 19 = 65 which becomes 65 = 65, confirming the first equation is true with those numbers.\r<BR>\n" );
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document.write( "u + 2b + 4s = 160 becomes 8 + 76 + 76 = 160 which becomes 160 = 160, confirming the second equation is true with those number.\r<BR>\n" );
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document.write( "in addition, the number of wheels on the bicycles is equal to the number of wheels on the skateboards which was one of the pieces of given information in the problem.\r<BR>\n" );
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document.write( "consequently, the solution is confirmed to be good.\r<BR>\n" );
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