document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190940>Question 1190940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Linda's age is twice her sister's age. Difference between their ages is a perfect square number. If the difference in their age is between 5 years and 40 years, what is the difference between the highest and the lowest possible values of Linda's age? </SPAN>\n" );
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document.write( "Edit: I changed the 40 to 36. I'm not sure why my brain went for that error initially.\r<BR>\n" );
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document.write( "Difference between their ages is a perfect square number. <BR>\n" );
document.write( "The difference in their age is between 5 years and 40 years.\r<BR>\n" );
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document.write( "Those two facts allow us to say that their age gap is one of the following numbers: 9, 16, 25, 36<BR>\n" );
document.write( "Simply list the perfect squares between 5 and 40.<BR>\n" );
document.write( "Later on, we'll only focus on the smallest and largest age gap. \r<BR>\n" );
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document.write( "x = sister's present day age<BR>\n" );
document.write( "2x = Linda's present day age\r<BR>\n" );
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document.write( "If Linda is 9 years older, then<BR>\n" );
document.write( "(linda's age) - (sister's age) = 9<BR>\n" );
document.write( "2x - x = 9<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "Telling us that the sister is 9 years old and Linda is 2*x = 2*9 = 18 years old.\r<BR>\n" );
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document.write( "Or if Linda is 36 years older, then you should find that x = 36 through similar steps. That would make Linda to be 2x = 2*36 = 72 years old.\r<BR>\n" );
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document.write( "Linda's lowest age = 18<BR>\n" );
document.write( "Linda's highest age = 80<BR>\n" );
document.write( "Difference = 72 - 18 = 54\r<BR>\n" );
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document.write( "Answer: 54<BR>\n" );
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