Answer:
I have $550; my sister has $300.
Explanation:
Let the amount I have be x.
Let the amount my sister has be y.
We have a total of $850, so
x + y = 850
50% of my amount plus 75% of my sister's amount equals $500.
0.5x + 0.75y = 500
We have a system of two equations:
x + y = 850
0.5x + 0.75y = 500
Multiply the second equation by 2 and subtract the first equation from it.
0.5y = 150
y = 300
x + y = 850
x + 300 = 850
x = 550
Answer: I have $550; my sister has $300.