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 x be the amount of money Ali and Samuel had at the beginning.
After Samuel gave $15 to Ali, Ali had x + 15 and Samuel had x - 15.
Given that the ratio of Ali's money to Samuel's was 7:5, we can write the following equation:
(x + 15) / (x - 15) = 7/5
Cross multiply to get:
5(x + 15) = 7(x - 15)
Expand the equation:
5x + 75 = 7x - 105
Subtract 5x from both sides:
75 = 2x - 105
Add 105 to both sides:
180 = 2x
Divide by 2:
x = 90
Therefore, Ali and Samuel each had $90 at the beginning.