SOLUTION: Scott and Laura have both invested some money. Scott invested $2,500 more than Laura and at a 2% higher interest rate. If Scott received $900 annual interest and Laura received $40

Let x be the the annual interest of the Scott's investment (as decimal).

Then Laura's annual interest is (x-0.02).


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    |  This variable x is the only unknown I will use in my solution.        |
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Then the  Scott's principal investment is  {{900/x}}}  dollars,

while the Laura's principal investment is    dollars.



According to the condition, the difference of their principals is 2500;

it gives you the core equation


     -  = 2500.      (1)


At this point, the setup is just completed, and now I start solving this equation.



First, divide by 100 both sides

     -  = 25.


Next, multiply both sides by x*(x-0.02) and simplify, step by step

    9*(x-0.02) - 4x = 25x*(x-0.02)

    9x - 0.18  - 4x = 25x^2 - 0.5x

       5x -0.18     = 25x^2 - 0.5x

       25x^2 - 5.5x + 0.18 = 0

     =  =  = .


So, there are two roots:   =  =  = 0.18,

                  and      =  =  = 0.04.


Both the roots satisfy the basic equation (1):

    x= 0.18:    -  = 5000 - 2500 = 2500 dollars.      ! correct !

and

    x= 0.14:    -  = 22500 - 20000 = 2500 dollars.    ! correct !


Thus for Scott's investment, we have two possible answers: a)   = 5000 dollars  and/or  b)  = 22500 dollars.