Question 110317
Dad's age is d, Melinda's age is m.
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{{{d=m+30}}} describes the situation now.
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{{{(d-8)=(m-8)^2}}} describes the situation 8 years ago.
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This seems to be a good candidate for solution by substitution, so substitute {{{m+30}}} for {{{d}}} in {{{(d-8)=(m-8)^2}}} making:
:
{{{(m+30-8)=(m-8)^2}}} , then simplify.
{{{m+22=m^2-16m+64}}}
{{{m^2-16m-m+64-22=0}}}
{{{m^2-17m+42=0}}}
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Then we factor:
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Since the sign on the m term is - and the sign on the constant term is +, we know that we are looking for factors of the form {{{(m-a)(m-b)}}}.
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The prime factors of 42 are 2, 3, and 7.  So, possible values for a and b are 1 and 42, 2 and 21, 3 and 14, and 6 and 7.  Of these possibilities, only 3 and 14 sum to 17, the coefficient on the m term, so our factors must be:
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{{{(m-3)(m-14)}}}.
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This means that Melinda is either 3 or 14.  But the answer 3 is not possible, because she wouldn't have been born 8 years previously.  Hence, the answer must be 14.
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Check:
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Melinda 14, Dad 44.
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Eight years ago, Melinda 6 and Dad 36, {{{6^2=36}}}, check.