document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011333>Question 1011333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cost of a small bottle of juice is $y<BR>\n" );
document.write( "the cost of a large bottle of juice is $(y+1)<BR>\n" );
document.write( "When Jade spends $36 on small bottles only, she receives 25 more bottles than when she spends $36 on large bottles only.<BR>\n" );
document.write( " (I) show that 25y^2+25y-36=0<BR>\n" );
document.write( " (II) Factorise 25y^2+25y-36=0<BR>\n" );
document.write( " (III) solve the equation 25y^2+25y-36=0<BR>\n" );
document.write( " (IV) find the total cost of 1 small bottle of juice and 1 large bottle of juice </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626957 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=626957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cost of a small bottle is y dollars.<BR>\n" );
document.write( "cost of a large bottle is (y+1) dollars.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2Fy ALIGN=MIDDLE  ALT=\"36%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of small bottles.<BR>\n" );
document.write( "this comes from the number of small bottle times the cost of each small bottle = 36 dollars.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F%28y%2B1%29 ALIGN=MIDDLE  ALT=\"36%2F%28y%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of large bottles.<BR>\n" );
document.write( "this comes from the number of large bottle times the cost of each large bottle = 36 dollars.\r<BR>\n" );
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document.write( "when she spends 36 dollars on small bottles, she has 25 more bottles than when she spends 36 dollars on large bottles.\r<BR>\n" );
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document.write( "that leads to the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2Fy+=+36%2F%28y%2B1%29+%2B+25 ALIGN=MIDDLE  ALT=\"36%2Fy+=+36%2F%28y%2B1%29+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that equation says that the number of small bottles is 25 more than the number of large  bottles.\r<BR>\n" );
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document.write( "you have the equation of:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2Fy+=+36%2F%28y%2B1%29+%2B+25 ALIGN=MIDDLE  ALT=\"36%2Fy+=+36%2F%28y%2B1%29+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply both sides of that equation by y * (y+1) to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836+%2A+%28y%2B1%29%29+=+%2836+%2A+y%29+%2B+%2825+%2A+%28y+%2A+%28y%2B1%29%29%29 ALIGN=MIDDLE  ALT=\"%2836+%2A+%28y%2B1%29%29+=+%2836+%2A+y%29+%2B+%2825+%2A+%28y+%2A+%28y%2B1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836+%2A+%28y%2B1%29%29+=+%2836+%2A+y%29+%2B+%2825+%2A+%28y%5E2%2By%29%29 ALIGN=MIDDLE  ALT=\"%2836+%2A+%28y%2B1%29%29+=+%2836+%2A+y%29+%2B+%2825+%2A+%28y%5E2%2By%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36y+%2B+36+=+36y+%2B+25y%5E2+%2B+25y ALIGN=MIDDLE  ALT=\"36y+%2B+36+=+36y+%2B+25y%5E2+%2B+25y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract the left side of the equation from both sides of the equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+36y+%2B+25y%5E2+%2B+25y+-+36y+-+36 ALIGN=MIDDLE  ALT=\"0+=+36y+%2B+25y%5E2+%2B+25y+-+36y+-+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the 36y and the -36y will cancel out when you combine like terms.\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+25y%5E2+%2B+25y+-+36 ALIGN=MIDDLE  ALT=\"0+=+25y%5E2+%2B+25y+-+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that's the same as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25y%5E2+%2B+25y+-+36+=+0 ALIGN=MIDDLE  ALT=\"25y%5E2+%2B+25y+-+36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you would factorize 25y^2 + 25y - 36 to get:\r<BR>\n" );
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document.write( "(5y+9) * (5y-4) = 0\r<BR>\n" );
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document.write( "this could be done using factoring techniques or through the use of the quadratic formula.\r<BR>\n" );
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document.write( "when you solve the equation of 25y^2 + 25y - 36, you set it equal to 0 and factorize it and then solve for y.\r<BR>\n" );
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document.write( "each of the factors is set to 0 to solve for y.\r<BR>\n" );
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document.write( "5y+9 = 0 gets you y = -9/5\r<BR>\n" );
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document.write( "5y-4 = 0 gets you y = 4/5\r<BR>\n" );
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document.write( "y has to be positive so y = 4/5.\r<BR>\n" );
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document.write( "that's the cost of a small bottle.\r<BR>\n" );
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document.write( "the cost of a large bottle would be 4/5 + 1 = 9/5.\r<BR>\n" );
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document.write( "4/5 of a dollar = $0.8 dollars = 80 cents.\r<BR>\n" );
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document.write( "9/5 of a dollar = $1.8 dollars = 1 dollar and 80 cents.\r<BR>\n" );
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document.write( "the cost of a small bottle = 80 cents.<BR>\n" );
document.write( "the cost of a large bottle = 1 dollar and 80 cents.\r<BR>\n" );
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document.write( "36/y = number of small bottles = 36/.8 = 45 small bottles.\r<BR>\n" );
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document.write( "36/(y+1) = 36/1.8 = 20 large bottles.\r<BR>\n" );
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document.write( "45 small bottles is 25 more than 20 large bottles.\r<BR>\n" );
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document.write( "the equation of 36/y = 36/(y+1) + 25 is good.\r<BR>\n" );
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document.write( "all of the questions have been answered.\r<BR>\n" );
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document.write( "1.<BR>\n" );
document.write( "we derived 25y^2 + 25y - 36 from 36/y = 36/(y+1) + 25<BR>\n" );
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document.write( "factors are (5y+9) * (5y-4)<BR>\n" );
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document.write( "we got y = -9/5 and y = 4/5 where y = 4/5 was the only valid solution.<BR>\n" );
document.write( "4.<BR>\n" );
document.write( "the cost of a small bottle is $0.8 and the cost of a large bottle is $1.8.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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