document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=849811>Question 849811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On Monday, the park was billed $315 to feed 21 coyotes and 21 lions. On Tuesday, the park was billed $484 to feed 28 coyotes and 36 lions. What is the cost to feed each lion and each coyote?\r<BR>\n" );
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document.write( "You get a notification that next week, the prices to feed both animals will increase by 5%. What will be the cost to feed 35 coyotes and 40 lions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511753 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=511753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = cost to feed coyotes and y = cost to feed lions.\r<BR>\n" );
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document.write( "on wednesday, 21x + 21y = 315\r<BR>\n" );
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document.write( "on tuesday, 28x + 36y = 484\r<BR>\n" );
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document.write( "solve these 2 equations simultaneously to find the value of x and y.\r<BR>\n" );
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document.write( "equations are:\r<BR>\n" );
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document.write( "21x + 21y = 315<BR>\n" );
document.write( "28x + 36y = 484\r<BR>\n" );
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document.write( "you can solve by substitution, or by elimination, or by graphing.\r<BR>\n" );
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document.write( "i'll solve by elimination.\r<BR>\n" );
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document.write( "least common multiple of 21 and 28 is 84.\r<BR>\n" );
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document.write( "multiply first equation by 4 and second equation by 3 to get:\r<BR>\n" );
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document.write( "84x + 84y = 1260<BR>\n" );
document.write( "84x + 108y = 1452\r<BR>\n" );
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document.write( "subtract first equation from the second to get:\r<BR>\n" );
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document.write( "24y = 192\r<BR>\n" );
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document.write( "divide 192 by 24 to get:\r<BR>\n" );
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document.write( "y = 8\r<BR>\n" );
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document.write( "now that you know the value of y, substitute for y in either equation to find the value of x.\r<BR>\n" );
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document.write( "substituting in 21x + 21y = 315 gets:\r<BR>\n" );
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document.write( "21x + 21(8) = 315<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "21x + 168  = 315<BR>\n" );
document.write( "subtract 168 from both sides of the equation to get:<BR>\n" );
document.write( "21x = 147<BR>\n" );
document.write( "divide both sides of the equation by 21 to get:<BR>\n" );
document.write( "x = 7\r<BR>\n" );
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document.write( "your answer should be:\r<BR>\n" );
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document.write( "x = 7 = cost to feed one coyote.<BR>\n" );
document.write( "y = 8 = cost to feed one lion.\r<BR>\n" );
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document.write( "confirm this solution is correct by substituting for x and y in both equations.\r<BR>\n" );
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document.write( "both original equations are:\r<BR>\n" );
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document.write( "21x + 21y = 315<BR>\n" );
document.write( "28x + 36y = 484\r<BR>\n" );
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document.write( "after substituting, these equations become:\r<BR>\n" );
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document.write( "21(7) = 21(8) = 315<BR>\n" );
document.write( "28(7) + 36(8) = 484\r<BR>\n" );
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document.write( "evaluate both equations to get:\r<BR>\n" );
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document.write( "315 = 315<BR>\n" );
document.write( "484 = 484\r<BR>\n" );
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document.write( "the solution is confirmed to be good.\r<BR>\n" );
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document.write( "x = 7<BR>\n" );
document.write( "y = 8\r<BR>\n" );
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document.write( "cost to feed one coyote = 7.<BR>\n" );
document.write( "cost to feed one lion = 8.\r<BR>\n" );
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document.write( "if the price is increased by 5%, then:\r<BR>\n" );
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document.write( "cost to feed one coyote becomes 7 + .05*7 = 7.35<BR>\n" );
document.write( "cost to feed one lion becomes 8 + .05*8 = 8.4.\r<BR>\n" );
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document.write( "the cost to feed 35 coyotes and 40 lions then becomes:\r<BR>\n" );
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document.write( "35(7.35) + 40(8.4) = 593.25\r<BR>\n" );
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document.write( " </SPAN>\n" );
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