SOLUTION: Charles is 4 years older than Jake. The product of Charles' age three years from now and Jake's age 2 years ago is 90. Find their present age.

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Question 1144020: Charles is 4 years older than Jake. The product of Charles' age three years from now and Jake's age 2 years ago is 90. Find their present age.
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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Let x be the Charles' age.  Then the Jake's age is (x-4).


Charles' age 3 years from now will be (x+3) years; Jake's age 2 years ago was ((x-4)-2) = (x-6) years.


We are given

     (x+3)*(x-6) = 90.


You can solve this quadratic equation using the quadratic formula.

Or you can solve it MENTALLY noticing that 90 is the product of the two factors (x+3)  and  (x-6), that differ by 9.

Then you get momentarily  x-6 = 6;  x+3 = 15,  which implies  x = 12.


ANSWER.  Charles is 12 years old;  Jake is 8 years old.


CHECK.   (12+3)*(8-2) = 15*6 = 90.    ! Correct !

Solved.