SOLUTION: jill is 8 years older than matt. the product of their ages is 65. what are their ages

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Question 857169: jill is 8 years older than matt. the product of their ages is 65. what are their ages
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let j = jill's age
Let m = Matt's age
The problem statement has
(1) j = m + 8 and
(2) j*m = 65
Put (1) into (2) and get
(3) (m+8)*m = 65 or
(4) m^2 + 8m -65 = 0 which factors to
(5) (m+13)*(m-5) = 0
Set each factor equal to zero and solve for m gives us
(6) m = (-13,5)
Since Matt cant be negative age we have
(7) m = 5
Then from (1) we get
(8) j = 5 + 8 or
(9) j = 13
Let's check this with (3).
Is ((8+5)*5 = 65)?
Is (13*5 = 65)?
Is (65 = 65)? Yes
Answer: Jill is 13 and Matt is 5.