document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252881>Question 252881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three boys have marbles in the ratio 19 : 5 : 3. If the boy with the least number has 9 marbles, how many marbles does the boy with the greatest number have?\r<BR>\n" );
document.write( "\n" );
document.write( "(A) 57    (B) 62    (C) 48    (D) 54    (E) 70<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185001 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=185001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let A be the one with the largest number.<BR>\n" );
document.write( "let B be the one with the middle number.<BR>\n" );
document.write( "let C be the one with the smallest number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let a = the number of marbles that A has.<BR>\n" );
document.write( "let b = the number of marbles that B has.<BR>\n" );
document.write( "let c = the number of marbles that C has.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a:b:c = 19:5:3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "C has 9 marbles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "9/3 = 3 which means that C has 3 times the marbles as it's ratio number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to keep the ratios intact, all others in the chain have to be multiplied by 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a:b:c = 19:5:3 = 57:15:9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that A has 57 marbles while B has 15 marbles while C has 9 marbles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also use the ratio formula to find the correct value.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b:c = 5:3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is the same as b/c = 5/3 since a fraction is a ratio of 2 numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have b/c = 5/3.<BR>\n" );
document.write( "you know that c = 9.<BR>\n" );
document.write( "the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b/9 = 5/3<BR>\n" );
document.write( "multiply both sides of this equation by 9 to get:<BR>\n" );
document.write( "b = (9*5)/3 = 45/3 = 15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now that you know b, you can solve for a in the same manner.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a:b = 19:5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is the same as a/b = 19/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have a/b = 19/5.<BR>\n" );
document.write( "you know that b is 15.<BR>\n" );
document.write( "the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a/15 = 19/5<BR>\n" );
document.write( "multiply both sides of this equation by 15 to get:<BR>\n" );
document.write( "a = (15*19)/5 = 285/5 = 57\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you wind up with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a = 57<BR>\n" );
document.write( "b = 15<BR>\n" );
document.write( "c = 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your question was how many marbles does the boy with the greatest number have?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your answer is selection A (57).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );