document.write( "Question 758092: the sum of the ages of the parents and the three children is decades over a century.
\n" ); document.write( "The father is twice as old as the eldest child.
\n" ); document.write( "When the eldest child was born, the sum of the parents age is 54.
\n" ); document.write( "When the youngest child was born, the sum of the parents age was 70.
\n" ); document.write( "In 38 years, the sum of the parents ages will be equal to the sum of the childrens ages.
\n" ); document.write( "How old is the second child?
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Algebra.Com's Answer #461316 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
the sum of the ages of the parents and the three children is decades
\n" ); document.write( "over a century.
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\n" ); document.write( "f, m, a, b, c; (a is the oldest child)
\n" ); document.write( "The father is twice as old as the eldest child.
\n" ); document.write( "f = 2a
\n" ); document.write( ":
\n" ); document.write( "When the eldest child was born, the sum of the parents age is 54.
\n" ); document.write( "(f-a) + (m-a) = 54,
\n" ); document.write( "f + m - 2a = 54
\n" ); document.write( "we know that f = 2a
\n" ); document.write( "2a + m - 2a = 54
\n" ); document.write( "m = 54 is mom's age
\n" ); document.write( ":
\n" ); document.write( "When the youngest child was born, the sum of the parents age was 70.
\n" ); document.write( "(f-c) + (m-c) = 70,
\n" ); document.write( "f + m - 2c = 70
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\n" ); document.write( "Use elimination with these two equations
\n" ); document.write( "f + m - 2c = 70
\n" ); document.write( "f + m - 2a = 54
\n" ); document.write( "---------------subtraction eliminates f and m
\n" ); document.write( "+2a - 2c = 16
\n" ); document.write( "simplify
\n" ); document.write( "a - c = 8
\n" ); document.write( "or
\n" ); document.write( "c = a - 8
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\n" ); document.write( "In 38 years, the sum of the parents ages will be equal to the sum
\n" ); document.write( " of the children's ages.
\n" ); document.write( "(f+38) + (m+38) = (a+38) + (b+38) + (c+38)
\n" ); document.write( "combine the values
\n" ); document.write( "f + m + 76 = a + b + c + 114
\n" ); document.write( "subtract 76 from both sides
\n" ); document.write( "f + m = a + b + c + 38
\n" ); document.write( "Replace f with 2a
\n" ); document.write( "2a + m = a + b + c + 38
\n" ); document.write( "subtract a from both sides and we have
\n" ); document.write( "a + m = b + c + 38
\n" ); document.write( "replace c with (a-8)
\n" ); document.write( "a + m = b + a - 8 + 38
\n" ); document.write( "subtract a from both sides
\n" ); document.write( "m = b + 30
\n" ); document.write( "We know that mom is 54
\n" ); document.write( "54 = b + 30
\n" ); document.write( "b = 54 - 30
\n" ); document.write( "b = 24 is the 2nd child's age
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\n" ); document.write( "Check this mess out by assuming the total of their present ages is
\n" ); document.write( "an even 10 (a decade) over 100 and a=30
\n" ); document.write( "f = 60 (2a)
\n" ); document.write( "m = 54
\n" ); document.write( "a = 30
\n" ); document.write( "b = 24 (m-30)
\n" ); document.write( "c = 22 (a-8)
\n" ); document.write( "-------
\n" ); document.write( "tot: 190\r
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