Question 1206851
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Question: 
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?


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x = Amount Ali ends up with = Amount Samuel ends up with


Rewind the clock so that Samuel gets his $15 back
Samuel's amount goes from x to x+15.
Ali's amount drops from x to x-15.




"The ratio of Ali's money to Samuel's was 7:5" means that,


Ali/Samuel = (x-15)/(x+15) = 7/5
That equation solves to x = -90 which makes no sense.


If instead the ratio was Samuel to Ali, then the equation would be (x+15)/(x-15) = 7/5 and that solves to x = 90.


It appears some typo is going on here.
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