document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189162>Question 1189162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rick combines 8 atoms of hydrogen and 4 atoms of oxygen to make 4 molecules of water. Write a direct variation equation that relates atoms of oxygen O to atoms of hydrogen H. How many hydrogen atoms does Rick need to form water molecules using 32 oxygen atoms? Graph the variation with hydrogen along the x-axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820423 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=820423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the direct variation formula is y = k * x\r<BR>\n" );
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document.write( "you start with:\r<BR>\n" );
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document.write( "4 molecules of water is equal to 8 atoms of hydrogen combined with 4 atoms of oxygen.\r<BR>\n" );
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document.write( "if you divide both sides of this equation by 4, you get:\r<BR>\n" );
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document.write( "1 molecule of water is equal to 2 atoms of hydrogen combined with 1 atom of oxygen.\r<BR>\n" );
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document.write( "that means that 1 molecule of water contains 3 atoms, 2 of which are hydrogen and 1 of which is oxygen.\r<BR>\n" );
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document.write( "your formula of y = k * x starts off as:\r<BR>\n" );
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document.write( "4 = k * 12\r<BR>\n" );
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document.write( "4 is your y which is equal to 4 molecules of water.\r<BR>\n" );
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document.write( "12 is your x which is equal to 8 atoms of hydrogen combined with 4 atoms of oxygen for a total of 12 atoms.\r<BR>\n" );
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document.write( "you solve for k to get:\r<BR>\n" );
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document.write( "k = 4/12 = 1/3.\r<BR>\n" );
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document.write( "your direct variation formula becomes:\r<BR>\n" );
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document.write( "y = 1/3 * x.\r<BR>\n" );
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document.write( "when the number of hydrogen atoms is 32, they are combined with 16 atoms of oxygen to get a total of 48 atoms.\r<BR>\n" );
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document.write( "your equation becomes y = 1/3 * 48.\r<BR>\n" );
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document.write( "solve for y to get y = 16.\r<BR>\n" );
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document.write( "when you have 32 atoms of hydrogen, that is combined with 16 atoms of oxygen to get 16 molecules of water.\r<BR>\n" );
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document.write( "you could also solve this in the following manner, which doesn't combine the atoms of hydrogen with the atoms of oxygen.\r<BR>\n" );
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document.write( "you start with:\r<BR>\n" );
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document.write( "y = k * x\r<BR>\n" );
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document.write( "y is equal to 4 molecules of water, which we'll call 4w.<BR>\n" );
document.write( "x is equal to 8 atoms of hydrogen combined with 4 atoms of oxygen which we'll call 8h + 4o.\r<BR>\n" );
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document.write( "y = k * x becomes:\r<BR>\n" );
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document.write( "4w = k * (8h + 4o)<BR>\n" );
document.write( "w equals one molecule of water.<BR>\n" );
document.write( "h = one atom of hydrogen.<BR>\n" );
document.write( "o = one atom of oxygen.\r<BR>\n" );
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document.write( "solve for k to get:\r<BR>\n" );
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document.write( "k = 4w / (8h + 3o)\r<BR>\n" );
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document.write( "divide numerator and denominator of the right side of this equation by 4 to get:\r<BR>\n" );
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document.write( "k = w / (2h + o)\r<BR>\n" );
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document.write( "your direct variation equation becomes:\r<BR>\n" );
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document.write( "y = w / (2h + o) * x\r<BR>\n" );
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document.write( "when y = 4w and x = (8h + 4o), the equation becomes:\r<BR>\n" );
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document.write( "4w = w / (2h + o) * (8h + 4o)\r<BR>\n" );
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document.write( "factor (8h + 4o) to have your equation becomes:\r<BR>\n" );
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document.write( "4w = w / (2h + o) * 4 * (2h + o)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "4w = 4w, confirming the value of k is correct.\r<BR>\n" );
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document.write( "when h becomes 32h, then o becomes 16o and the formula becomes:\r<BR>\n" );
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document.write( "y = k * (32h + 16o) which becomes:\r<BR>\n" );
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document.write( "y = w / (2h + o) * (32h + 16o)\r<BR>\n" );
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document.write( "factor (32h + 16o) to make your equation become:\r<BR>\n" );
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document.write( "y = w / (2h + o) * 16 * (2h + o)\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = 16w\r<BR>\n" );
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document.write( "same answer:\r<BR>\n" );
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document.write( "when you have 32 atoms of hydrogen, you get 16 molecules of water that are equal to 32 atoms of hydrogen combined with 16 atoms of oxygen.\r<BR>\n" );
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document.write( "the first thing i did above was simpler, because 8 atoms of hydrogen plus 4 atoms of oxygen equals 12 total atoms.\r<BR>\n" );
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document.write( "the second thing i did was to show you that, even if you didn't combine hydrogen and oxygen atoms together, you'd get the same answer.\r<BR>\n" );
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document.write( "go with the first thing i did that was:\r<BR>\n" );
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document.write( "y = k * x becomes:<BR>\n" );
document.write( "4 = k * 12.\r<BR>\n" );
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document.write( "you solve for k to get:\r<BR>\n" );
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document.write( "k = 1/3\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "y = 1/3 * x\r<BR>\n" );
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document.write( "when x = 48 total atoms (32 hydrogen plus 16 oxygen), you get:\r<BR>\n" );
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document.write( "y = 1/3 * 48 = 16.\r<BR>\n" );
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document.write( "you graph:\r<BR>\n" );
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document.write( "y = 1/3 * x, which is shown below:\r<BR>\n" );
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document.write( "x represents the total number of atoms in 1 molecule of water, which is 3.<BR>\n" );
document.write( "y represents the total number of molecules of water.\r<BR>\n" );
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document.write( "when you have 12 atoms, 8 of which are hydrogen and 4 of which are oxygen, you get 4 molecules of water.<BR>\n" );
document.write( "that's why the coordinate point is (12,4).<BR>\n" );
document.write( "that's a total of 12 atoms to 4 molecules of water, 8 of the 12 atoms being hydrogen and 4 of the 12 atoms being oxygen.\r<BR>\n" );
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document.write( "when you have a total of 48 atoms, 32 of which are hydrogen and 16 of which are oxygen, you get 16 molecules of water.<BR>\n" );
document.write( "that's represented by the coordinate point of (48,16).\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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