SOLUTION: Melinda's dad is 30 years older than Melinda is now. Eight years ago, his age was equal to the squaer of Melinda's age then. How old is Melinda now?

Question 110317: Melinda's dad is 30 years older than Melinda is now. Eight years ago, his age was equal to the squaer of Melinda's age then. How old is Melinda now?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Dad's age is d, Melinda's age is m.
:
describes the situation now.
:
describes the situation 8 years ago.
:
This seems to be a good candidate for solution by substitution, so substitute for in making:
:
, then simplify.

:
Then we factor:
:
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 .
:
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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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:
:
Melinda 14, Dad 44.
:
Eight years ago, Melinda 6 and Dad 36, , check.

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