SOLUTION: John is 5 years older than AL. Two years ago the product of their ages was 30 less than it is now. How old are they now?

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Question 54443: John is 5 years older than AL. Two years ago the product of their ages was 30 less than it is now. How old are they now?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
John is 5 years older than AL. Two years ago the product of their ages was 30 less than it is now. How old are they now?
---------
NOW Data:
Let Al be "x" yrs. old.
Then John is "x+5" yrs. old.
---------
TWO YEARS AGO DATA:
Al was "x-2" yrs. old.
John was "x+3" yrs. old.
---------
EQUATION;
(x-2)(x+3)=?
Here the problem becomes ambiguous.
It says "Two years ago the product of
their ages was 30 less than WHAT is now.
Is WHAT the product now?
Is WHAT the sum now?
What is WHAT?
Cheers,
Stan H.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
John is 5 years older than AL. Two years ago the product
of their ages was 30 less than it is now. How old are 
they now?

John's age now = J
Al's age now = A
John's age two years ago = J-2
Al's age two years ago = A-2
Product of their ages now = JA
Product of their ages two years ago = (J-A)(A-2) 

>>...John is 5 years older than AL.

J = A + 5

>>...Two years ago the product of their ages was 30 less 
than it is now...<<

(J-2)(A-2) = JA - 30

Simplify that equation

JA - 2J - 2A + 4 = JA - 30
Subtract JA from both sides

    -2J - 2A + 4 = -30

        -2J - 2A = -34

So now you have the system of equations

               J = A + 5 
        -2J - 2A = -34

Can you solve that system?  If not post again.

  J = 11,  A = 6

Checking:
 11 is indeed 5 more than 6.
 The product of their ages now = 11×6 = 66
 The product of their ages two years ago = 9×4 = 36
 And sure enough, 36 was 30 less than 66. 

Edwin
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