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