SOLUTION: Maria's age is M. Pat's age is M+3. Five years ago, the product of their ages was 70. How old is Maria now

Question 774420: Maria's age is M. Pat's age is M+3. Five years ago, the product of their ages was 70. How old is Maria now
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
This is a little tricky involving a quadratic. Can you factor a quadratic?
Let m = Maria's current age
Let p = Pat's current age
Then we have
(1) p = m +3 and
(2) (m-5)*(p-5) = 70
Now put (1) into (2) to get
(3) (m-5)*(m+3-5) = 70 or
(4) (m-5)*(m-2) = 70 or
(5) m^2 -5m - 2m + 10 = 70 or
(6) m^2 -7m -60 = 0 which factors to
(7) (m-12)*(m+5) = 0
Select the positive root to get
(8) m = 12
Then
(9) p = 15
Is ((12-5)*(15-5) = 70)?
Is (7*10 = 70)?
Is (70 = 70)? Yes
Answer: Maria is currently 12 years of age.
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