document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081008>Question 1081008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jack and Miya had some cards.In a game,Jack lost 1/10 of his card to Miya. After Jack lost his cards to Miya,the ratio of the number of cards jack had to the number of cards Miya had was 3:1.The next day, after jack lost more cards to Miya, the ratio became 4:7 and Miya had 72 more cards than jack.a) what was the ratio of the number of cards jack had to the number of cards Miya had at first b)how many cards did Miya win from jack altogether  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695165 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Jack and Miya had some cards.<BR>\n" );
document.write( "In a game, Jack lost 1/10 of his card to Miya.<BR>\n" );
document.write( " After Jack lost his cards to Miya,the ratio of the number of cards jack had to the number of cards Miya had was 3:1.<BR>\n" );
document.write( "The next day, after jack lost more cards to Miya, the ratio became 4:7 and Miya had 72 more cards than jack.<BR>\n" );
document.write( "a) what was the ratio of the number of cards jack had to the number of cards Miya had at first<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let j = no. of cards J had originally<BR>\n" );
document.write( "let m = no. of cards M had<BR>\n" );
document.write( "\" Jack lost 1/10 of his card to Miya. After Jack lost his cards to Miya, the ratio of the number of cards jack had to the number of cards Miya had was 3:1.\"<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.9j%29%2F%281.1m%29 ALIGN=MIDDLE  ALT=\"%28.9j%29%2F%281.1m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1 ALIGN=MIDDLE  ALT=\"3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "1(.9j) = 3(1.1m)<BR>\n" );
document.write( ".9j = 3.3m<BR>\n" );
document.write( "\"jack lost more cards to Miya, the ratio became 4:7\"<BR>\n" );
document.write( "let x = no. of more lost to Miya<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.9j-x%29%2F%281.1m%2Bx%29 ALIGN=MIDDLE  ALT=\"%28.9j-x%29%2F%281.1m%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replace .9j with 3.3m<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283.3m-x%29%2F%281.1m%2Bx%29 ALIGN=MIDDLE  ALT=\"%283.3m-x%29%2F%281.1m%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "7(3.3m-x) = 4(1.1m+x)<BR>\n" );
document.write( "23.1m - 7x = 4.4m + 4x<BR>\n" );
document.write( "23.1m - 4.4m = 4x + 7x<BR>\n" );
document.write( "18.7m = 11x<BR>\n" );
document.write( "\" and Miya had 72 more cards than jack.<BR>\n" );
document.write( "(1.1m + x) - (.9j-x) = 72<BR>\n" );
document.write( "1.1m - .9j + x + x = 72<BR>\n" );
document.write( "1.1m - .9j + 2x = 72<BR>\n" );
document.write( "replace .9j with 3.3m, replace x with .9m<BR>\n" );
document.write( "1.1m - 3.3m + 2(.9m) = 72<BR>\n" );
document.write( "1.1m - 3.3m + 1.8m = 72<BR>\n" );
document.write( "-2.2m + 2x = 72<BR>\n" );
document.write( "2x = 2.2m + 72<BR>\n" );
document.write( "divide by 2<BR>\n" );
document.write( "x = 1.1m + 36<BR>\n" );
document.write( "Using the equation 18.7m = 11x, replace x with 1.1m+36<BR>\n" );
document.write( "18.7m = 11(1.1m + 36)<BR>\n" );
document.write( "18.7m = 12.1m + 396<BR>\n" );
document.write( "18.7m - 12.1m = 396<BR>\n" );
document.write( "6.6m = 396<BR>\n" );
document.write( "m = 396/6.6<BR>\n" );
document.write( "m = 60 cards Miya originally<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".9j = 3.3(60)<BR>\n" );
document.write( "j = 198/.9<BR>\n" );
document.write( "j = 220 cards Jack originally<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) what was the ratio of the number of cards jack had to the number of cards Miya had at first<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220%2F60 ALIGN=MIDDLE  ALT=\"220%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 11:3<BR>\n" );
document.write( ":<BR>\n" );
document.write( " b)how many cards did Miya win from jack altogether <BR>\n" );
document.write( "First time: .1(220) = 22 cards<BR>\n" );
document.write( "2nd time: find x,we know:<BR>\n" );
document.write( "11x = 18.7m<BR>\n" );
document.write( "11x = 18.7(60)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1122%2F11 ALIGN=MIDDLE  ALT=\"1122%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 102 cards<BR>\n" );
document.write( "Total cards won by Miya; 22 + 102 = 124 cards<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "\n" );
document.write( "  </SPAN>\n" );
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