I presume that her entire course grade is comprised of her current grade and her midterm exam grade. If so, since her midterm grade is 10% of the entire grade, that must mean her current grade is worth 90%.
Course grade = 10%m + 90%*85
Grade = 0.1m + 76.5
If the course grade must be at least 89.5, then:
89.5 = 0.1m + 76.5
Subtract 76.5 from both sides of the above equation:
13 = 0.1m
Divide both sides by 0.1:
m = 130
Unless there is a lot of extra credit on the final, it looks like getting an A is this course is not likely to happen.
130 = m