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Achilles was trying to figure out the ages of three commanders Alexander, Bart, and Cicero, in his army.
\n" ); document.write( " The sum of their ages was 80; Alexander was two years younger than Bart, and the sum of the ages of Alexander and Bart was 20 more than the age of Cicero.
\n" ); document.write( " What are their ages?
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "\" The sum of their ages was 80;\"
\n" ); document.write( "a + b + c = 80
\n" ); document.write( ":
\n" ); document.write( "\" Alexander was two years younger than Bart,\"
\n" ); document.write( "a = b - 2
\n" ); document.write( "a - b = -2
\n" ); document.write( ":
\n" ); document.write( "\"the sum of the ages of Alexander and Bart was 20 more than the age of Cicero.\"
\n" ); document.write( "a + b = c + 20
\n" ); document.write( "a + b - c = 20
\n" ); document.write( "Subtract this equation from the 1st equation
\n" ); document.write( "a + b + c = 80
\n" ); document.write( "a + b - c = 20
\n" ); document.write( "-----------------subtraction eliminates a and b, find c
\n" ); document.write( "2c = 60
\n" ); document.write( "c = 30 yrs is C's age
\n" ); document.write( "then
\n" ); document.write( "a + b + 30 = 80
\n" ); document.write( "add to the 2nd equation
\n" ); document.write( "a + b = 50
\n" ); document.write( "a - b = -2
\n" ); document.write( "------------adding eliminates b, find a
\n" ); document.write( "2a = 48
\n" ); document.write( "a = 24
\n" ); document.write( "I'll let you find b\r
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