Answer: $370
===========================================================
Step-by-step explanation:
Hakim and Aziz have savings in the ratio 3:5. This means that Hakim has 3x dollars while Aziz has 5x dollars. The x is some positive real number.
We're then told that Hakim saved another $82, which means it goes from 3x to 3x+82
At the same time, Aziz spent $110 which means the 5x decreases to 5x-110
At this point, the two people have the same amount of money. Set the expressions we found equal to one another and solve for x.
3x+82 = 5x-110
3x-5x = -110-82
-2x = -192
x = -192/(-2)
x = 96
Then use this x value to compute each expression like so
- 3x+82 = 3*96+82 = 370
- 5x-110 = 5*96-110 = 370
Both have $370 after Hakim saved that additional $82 and after Aziz spent that $110.
------------------
Extra info:
If we rewind things a bit, Hakim would have 3*x = 3*96 = 288 dollars while Aziz would have 5x = 5*96 = 480 dollars. This is before any additional saving or spending.
Then note how the ratio 288:480 fully reduces to 3:5 after dividing both parts by the GCF 96.