document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285793>Question 285793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of three numbers is 98. The first number is 2/3 of the second, and the second is 5/8 of the third. What is the second number?\r<BR>\n" );
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document.write( "A. 18   B. 20   C. 30   D. 48  E. None of these. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207208 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=207208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sum of 3 number is 98.<BR>\n" );
document.write( "x = first number<BR>\n" );
document.write( "y = second number<BR>\n" );
document.write( "z = third number\r<BR>\n" );
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document.write( "x = (2/3)*y\r<BR>\n" );
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document.write( "y = (5/8)*z\r<BR>\n" );
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document.write( "x + y + z = 98\r<BR>\n" );
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document.write( "Since y = (5/8) * z, the equation becomes:\r<BR>\n" );
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document.write( "x + (5/8)*z + z = 98\r<BR>\n" );
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document.write( "Since x = (2/3) * y, and y = (5/8) * z, this means that:\r<BR>\n" );
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document.write( "x = (2/3)*(5/8)*z.\r<BR>\n" );
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document.write( "Substitute that value into the equation, and the equation becomes:\r<BR>\n" );
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document.write( "(2/3)*(5/8)*z + (5/8)*z + z = 98\r<BR>\n" );
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document.write( "You can factor out the z to get:\r<BR>\n" );
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document.write( "z * ((2/3)*(5/8) + (5/8) + 1) = 98\r<BR>\n" );
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document.write( "Simplify this equation to get:\r<BR>\n" );
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document.write( "z * ((10/24) + (5/8) + (8/8)) = 98\r<BR>\n" );
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document.write( "Simplify further to get:\r<BR>\n" );
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document.write( "z * ((10/24) + (15/24) + (24/24)) = 98\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "z * (49/24) = 98\r<BR>\n" );
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document.write( "Divide both sides of this equation by (49/24) to get:\r<BR>\n" );
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document.write( "z = 98 / (49/24) which is the same as:\r<BR>\n" );
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document.write( "z = 98 * (24/49).\r<BR>\n" );
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document.write( "Simplify this to get:\r<BR>\n" );
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document.write( "z = 2*24 = 48\r<BR>\n" );
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document.write( "Since z = 48, and y = (5/8)*z, this means that y = (5/8)*48 = 5*6 = 30.\r<BR>\n" );
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document.write( "You have:\r<BR>\n" );
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document.write( "z = 48<BR>\n" );
document.write( "y = 30\r<BR>\n" );
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document.write( "Since y = 30, and x = (2/3)*y, this means that x = (2/3)*30 = 20.\r<BR>\n" );
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document.write( "You have:\r<BR>\n" );
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document.write( "z = 48<BR>\n" );
document.write( "y = 30<BR>\n" );
document.write( "x = 20\r<BR>\n" );
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document.write( "To confirm these are accurate, substitute in your original equation to see if that equation is true using these values.\r<BR>\n" );
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document.write( "Your original equation is:\r<BR>\n" );
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document.write( "x + y + z = 98\r<BR>\n" );
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document.write( "That becomes:\r<BR>\n" );
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document.write( "20 + 30 + 48 = 98 which becomes 98 = 98 which is true.\r<BR>\n" );
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document.write( "These values are good for the sum equation.\r<BR>\n" );
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document.write( "Substitute in the piece part equations to see if they still hold up.\r<BR>\n" );
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document.write( "The first piece part is x = 2/3 * y.\r<BR>\n" );
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document.write( "Since 20 = 2/3 * 30 is true, this part is good.\r<BR>\n" );
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document.write( "The second piece part is y = (5/8) * z.\r<BR>\n" );
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document.write( "Since 30 = 5/8 * 48, this part is also good.\r<BR>\n" );
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document.write( "The solutions of:\r<BR>\n" );
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document.write( "x = 20<BR>\n" );
document.write( "y = 30<BR>\n" );
document.write( "z = 48\r<BR>\n" );
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document.write( "are all good.\r<BR>\n" );
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document.write( "The answer to your question is:\r<BR>\n" );
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document.write( "The second number is 30.\r<BR>\n" );
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document.write( "That would be selection C.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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