SOLUTION: Anton is four years older than Lisa. The product of his age 3 years from now and Lisa 's age two years ago is 90 years. Find their present age.

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Question 1050741: Anton is four years older than Lisa. The product of his
age 3 years from now and Lisa 's age two years ago is 90
years. Find their present age.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Anton is four years older than Lisa. The product of his
age 3 years from now and Lisa 's age two years ago is 90
years. Find their present age. 
Lisa's present age = L

Anton is four years older than Lisa.
Anton's present age = L+4
Anton's age 3 years from now = (L+4)+3 = L+4+3=L+7
Lisa's age 2 years ago = L-2

The product of his age 3 years from now and Lisa's age two years ago is 90 years


%28L%2B7%29%28L-2%29%22%22=%22%2290

Use FOIL on the left

L%5E2%2B5L-14%22%22=%22%2290

Get 0 on the right by subtracting 90 from both 
sides:

L%5E2%2B5L-104%22%22=%22%220

The factor pairs that have product 104 are

104×1, 52×2, 26×4, 13×8

Only 13 and 8 have difference 5.  So we factor

%28L%2B13%29%28L-8%29%22%22=%22%220

L+13 = 0;     L-8 = 0
   L = -13      L = 8

Ignore the negative answer.

Lisa's present age = L = 8

Anton's age = L+4 = 8+4 = 12



And indeed 15×6 = 90.

Edwin