SOLUTION: lean and Terry shared a sum of money. lean's share was $180 less than Terry's share. After Terry gave 1/7 of his share to Lean , lean had $20 more than Terry. How much did Lean hav

Let L be the amount of money that Lean  had at first;

    T be the amount of money that Terry had at first.


From the condition, we write first equation in the form

    T - L = 180  dollars.    (1)


After exchange, Terry had    dollars;  Lean had    dollars, 
and we have second equation

     -  = 20  dollars.   (2)


We can re-write equation (2) equivalently in the form

     = 20,

or, multiplying by 7, in the form

    7L - 5T = 140.             (3)


So, (1) and (3) are the equations to solve simultaneously.

Express T = L + 180 from (1) and substitute it into equation (3)

    7L - 5*(L+180) = 140,

    7L - 5L = 140 + 5*180

      2L    =    1040

       L    =    1040/2 = 520.


ANSWER.  Lean had $520 at first.

Let original amount Lean had, be L
Then original amount Terry had was: L + 180
After receiving  of Terry's, Lean then had: 
After giving  to Lean, Terry had:  remaining
                         We then get: 
                                     L + 180 + 7L = 6L + 1,080 + 140 ------ Multiplying by LCD, 7
                                      L + 7L - 6L = 1,080 + 140 - 180
                                               2L = 1,040
                  Original amount Lean had, or