document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207224>Question 1207224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tommy’s age is 2/3 Ben’s age now. In 8 years time, the ratio of Tommy’s age to Ben’s age will be 10:13. How old is Tommy now? </SPAN>\n" );
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document.write( "Answer: <font color=red>12</font> \r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "The ratio of their future ages, Tommy to Ben, is 10:13<BR>\n" );
document.write( "That scales to 10x:13x for some positive integer x.\r<BR>\n" );
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document.write( "Subtract 8 from each to get their present day age.<BR>\n" );
document.write( "Tommy = 10x-8<BR>\n" );
document.write( "Ben = 13x-8\r<BR>\n" );
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document.write( "We're told that Tommy's current age is 2/3 of Ben's current age.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "Tommy = (2/3)*( Ben )<BR>\n" );
document.write( "10x-8 = (2/3)*( 13x-8 )<BR>\n" );
document.write( "3(10x-8) = 2(13x-8)<BR>\n" );
document.write( "30x-24 = 26x-16<BR>\n" );
document.write( "30x-26x = -16+24<BR>\n" );
document.write( "4x = 8<BR>\n" );
document.write( "x = 8/4<BR>\n" );
document.write( "x = 2\r<BR>\n" );
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document.write( "Then compute 10x-8.<BR>\n" );
document.write( "10x-8 = 10*2-8 = 20-8 = <font color=red>12</font> is the answer.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Ben would be currently 18 since 13x-8 = 13*2-8 = 26-8 = 18<BR>\n" );
document.write( "Note that 12 is 2/3 that of 18, which helps partially confirm the answer.<BR>\n" );
document.write( "In other words, 12/18 = 2/3.<BR>\n" );
document.write( "Add 8 to each present day age to find that Tommy and Ben will be 12+8 = 20 and 18+8 = 26 respectively.<BR>\n" );
document.write( "The ratio 20:26 reduces to 10:13 when dividing both parts by the GCF 2.<BR>\n" );
document.write( "The answer is fully confirmed.<BR>\n" );
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