Isolating a quantity
SAT glossary · Course Foundations
Definition
The all-letters item type — 'which of the following expresses r in terms of A, P, and t' — with no arithmetic, no graph, and no numbers for Desmos to plot, which is exactly why it is a permanent resident of hard Module 2: the difficulty migrated to where the calculator cannot follow. The doctrine: treat every letter except your target as if it were a number; A=P(1+rt) is the same problem as 20=5(1+2r).
Isolating a quantity in plain English
Some questions give you an equation made up entirely of letters — like 'solve for r in terms of A, P, and t' — with no actual numbers to plug in and nothing to graph, which means calculator tools like Desmos are completely useless here. That's exactly why these show up in the harder part of the test: the difficulty has been moved to a place the calculator simply can't follow you. The trick to handling them calmly is to treat every letter EXCEPT the one you're solving for as if it were just some ordinary number — so an equation like A=P(1+rt), once you stop being intimidated by the extra letters, is really the exact same kind of problem as 20=5(1+2r), just solving for r using regular algebra steps (divide, subtract, etc).
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