Chaining a real running average into a real final-exam target
Three graded components — 82, 75, and 88, weighted at 25%, 25%, and 20% (summing to 70%, with the final exam's remaining 30% not yet included) — average to a real 81.21% overall so far. Feeding that real 81.21% into the final grade calculator as the current average, with the final worth 30% of the overall grade and a target of 85% overall, gives a real required final exam score of 93.84%.
Why this two-step process reflects how the numbers actually work
The weighted grade calculator only knows about the components it's given — it has no concept of a "final exam" separate from any other component. Deliberately leaving the final's weight out of the first calculation (using only the 70% already accounted for) produces exactly the "current average excluding the final" figure the second calculator needs as its starting point.
Why getting this chain right matters
Including the final exam's weight in the first calculation (treating it as a fourth component with, say, a score of 0) would corrupt the current-average figure and produce a wrong required-score result from the second calculator. The two calculators only compose correctly when the first one's weights genuinely represent everything already graded, and nothing more.
A practical way to use this chain during a semester
A student partway through a course can compute their real running average as each component is graded, then immediately check what the remaining final (or any remaining weighted component) would need to reach a specific target grade — turning a vague "how am I doing" question into a concrete, real number to aim for.