x = Ali's money at the beginning;
y = Sam's money at the beginning.


We have these two equations

    y - 15 = x + 15    (1)    "Ali and Samuel both had the same amount of money after Samuel gave $15 to Ali"

and 

     =     (2)    "The ratio of Ali's money to Samuel's was 7:5"


From (2),  x = .  Substitute it into equation (1).  You will get

    y - 15 =  + 15.


Multiply both sides by 5

    5y - 15*5 = 7y + 15*5

    5y - 75 = 7y + 75

    -75 - 75 = 7y - 5y

       -150  =    2y

          y  =  = -75.


But this answer, y = -75, is mathematically non-sensical, since the amount of money must be positive, in this context.


It means that the problem, as it is given in the post, is posed INCORRECTLY.

https://brainly.com/question/50102906?answeringSource=feedPublic%2FhomePage%2F9


Help please I don't understand
Ali and Samuel both had the same amount of money after Samuel gave $15 to Ali.
The ratio of Ali's money to Samuel's was 7:5. How much did each of them have at the beginning?

There obviously is some confusion here which is understandable. This is because  it should read: 
Help please I don't understand
Ali and Samuel both had the same amount of money. After Samuel gave $15 to Ali, the ratio of Ali's
money to Samuel's was 7:5. How much did each of them have at the beginning?

Let the original amount each had, be A
After giving $15 to Ali, Samuel had A - 15 remaining
After receiving $15 from Samuel, Ali had A + 15 
Since the ratio of Ali's money to Samuel's money - after the transfer - was 7:5, we get the
following PROPORTION, 
                    5(A + 15) = 7(A - 15) ----- Cross-multiplying
                      5A + 75 = 7A - 105
                      5A - 7A = - 105 - 75
                         - 2A = - 180
Amount each began with, or