A student's final grade is based 70% on exams (average 82) and 30% on homework (average 95). What is the student's weighted final grade?

A weighted average multiplies each score by its weight and adds: $0.70(82)+0.30(95)=57.4+28.5=85.9$, choice A. Because exams count more, the result is closer to $82$ than to $95$. Choice B ($88.5$) is the simple average, $\frac{82+95}{2}$, which gives the two parts equal weight. Choice D ($91.0$) reverses the weights, putting $70\%$ on homework (this gives $91.1$). Choice C ($89.0$) is not produced by either set of weights. Check the reasonableness: the weighted average must lie between $82$ and $95$ and nearer the more heavily weighted number.