SOLUTION: A cash register contains only five dollar and ten dollar bills. It contains 19 more five dollar bills than ten dollar bills, and the total amount of money in the cash register is $

Let x = the number of the 5-dollar bills, and
let y = the number of the 10-dollar bills.


Then from the condition you have these two equations

     x -   y =  19      (1)    ("19 more five dollar bills than ten dollar bills")
   5x  + 10y = 530      (2)    ("the total amount of money in the cash register is $530")


From equation (1) express x = 19 + y  and substitute it into equation (2).
You will get


    5*(19+y) + 10y = 530,    (3)

    95 + 5y + 10y = 530,

    15y = 530 - 95 = 435  

      y =  = 29.


Answer.  29 10-dollar bills  and  29 + 19 = 48 5-dollar bills.


Check.   10*29 + 5*48 = 530 dollars total.   ! Correct !

Let y = the number of the 10-dollar bills.

Then the number of the 5-dollar bills is (y+19), according to the condition.


10-dollar bills contribute  10*y     dollars to the total.

5-dollar  bills contribute  5*(y+19) dollars to the total.


So the money equation for the total is


    10y + 5*(y+19) = 530.


It is THE SAME EQUATION as  equation (3) in the Solution 1 above.

You can solve it by the same way, and you will get the same answer.