document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120664>Question 1120664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The present ages of two brothers are in the ratio of 7:8.Twenty years ago, the ratio of their ages was 9:11. Find the present age of the older brother  </SPAN>\n" );
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document.write( "Their ages 20 years ago were in the ratio 9:11.  So let their ages then be 9x and 11x.<br><BR>\n" );
document.write( "It is a typical way to start work on a problem where a ratio is given.<br><BR>\n" );
document.write( "Then their current ages are 9x+20 and 11x+20; and those ages are in the ratio 7:8.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%2B20%29%2F%2811x%2B20%29+=+7%2F8 ALIGN=MIDDLE  ALT=\"%289x%2B20%29%2F%2811x%2B20%29+=+7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77x%2B140+=+72x%2B160 ALIGN=MIDDLE  ALT=\"77x%2B140+=+72x%2B160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+20 ALIGN=MIDDLE  ALT=\"5x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Their ages 20 years ago were 9x=36 and 11x=44; their ages now are 36+20=56 and 44+20=64.<br><BR>\n" );
document.write( "Answer: The older brother is now 64.<br><BR>\n" );
document.write( "You should know how to solve a problem like this using formal algebra; however, I always like to encourage students to try to solve a problem informally using logical reasoning -- it's good brain exercise.<br><BR>\n" );
document.write( "In this problem, we know their ages 20 years ago were in the ratio 9:11; that means the older brother's age was a multiple of 11.<br><BR>\n" );
document.write( "And we know that now the ratio of their ages is 7:8, so the older brother's age now is a multiple of 8.<br><BR>\n" );
document.write( "So we only need to find a multiple of 11 which increased by 20 is a multiple of 8.<br><BR>\n" );
document.write( "11+20 = 31  nope...<BR>\n" );
document.write( "22+20 = 42  nope...<BR>\n" );
document.write( "33+20 = 53  nope...<BR>\n" );
document.write( "44+20 = 64  yep!!<br><BR>\n" );
document.write( "The older brother is now 64. </SPAN>\n" );
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