After a 20% sale discount, Frank purchased a new refrigerator for $850. How much did he save from the original price?

Frank saved $212.50 from the original refrigerator price because the $850 purchase amount represents 80% of the original price after a 20% discount was applied, requiring calculation of the full pre-discount value before determining the absolute savings amount through subtraction or direct percentage application to the original price.

The mathematical relationship establishes that 0.80 × original price = $850, leading to an original price of $1,062.50, from which the $850 paid is subtracted to yield the $212.50 savings figure.

A. $170

This amount represents exactly 20% of the discounted purchase price ($850 × 0.20 = $170), reflecting a pervasive computational error where students mistakenly apply the discount percentage to the sale price rather than the original price. This misconception violates fundamental discount mathematics principles, as percentage discounts always reference the pre-discount value the baseline from which reduction occurs. While $170 constitutes a mathematically coherent calculation, it answers a different question than what was posed: "What is 20% of $850?" rather than "What absolute dollar amount was removed from the original price to yield $850?" This option serves as an exceptionally effective distractor targeting the most common student error in percentage discount problems, revealing whether learners understand the directional relationship between original values, percentages, and resulting amounts.

B. $212.50

This value correctly represents the absolute dollar savings through proper discount mathematics application executed via two verification pathways. Primary method: recognizing $850 constitutes 80% of original price (100% - 20% discount), establishing equation 0.80P = 850; solving yields P = 850 ÷ 0.80 = $1,062.50 original price; savings = $1,062.50 - $850 = $212.50. Verification method: calculating 20% directly of original price ($1,062.50 × 0.20 = $212.50), confirming consistency between subtraction and percentage approaches. This dual-path validation demonstrates comprehensive understanding of percentage relationships specifically that discounts reduce original values while sale prices represent residual percentages. The precise decimal representation ($212.50 rather than rounded $213) reflects appropriate monetary precision standards, acknowledging cents-level accuracy in financial transactions while avoiding unwarranted significant figure inflation.

C. $105.75

This figure appears disconnected from standard discount calculation pathways involving the given values, lacking direct mathematical relationship to either $850 or $1,062.50 through simple percentage operations. Potential error origins include: misapplying compound discount formulas (850 × 0.80 × 0.155 ≈ 105.40 with rounding), confusing tax calculation with discount mechanics (850 × 0.1244 ≈ 105.75 representing hypothetical 12.44% tax misapplied), or executing multi-step arithmetic errors involving unnecessary division operations (850 ÷ 8 = 106.25 then subtracting 0.50). The value's proximity to one-eighth of the sale price (850 ÷ 8 = 106.25) suggests possible fraction-percentage confusion where students misinterpret "20%" as "⅛" (12.5%) then miscalculate. This option functions primarily as a random distractor without strong foundation in typical student error patterns, though it may trap learners employing unstructured guesswork rather than systematic problem-solving approaches.

D. $200

This amount represents a rough approximation emerging from mental estimation strategies specifically rounding $850 to $1,000 and calculating 20% as $200 then failing to adjust for the $150 rounding differential. While estimation skills hold educational value in appropriate contexts requiring rapid approximation, this question demands exact calculation rather than estimation. The $200 figure underestimates actual savings by $12.50 (approximately 5.9% error), demonstrating how rounding intermediate values before completing calculations introduces meaningful computational drift. This option targets students who prioritize computational speed over precision, misunderstand when estimation versus exact computation is appropriate, or lack confidence in decimal division operations (850 ÷ 0.80) preferring whole-number approximations despite explicit problem requirements for accurate financial determination. The persistent appeal of round numbers in financial contexts makes this a psychologically compelling but mathematically deficient choice.

Conclusion

The $212.50 savings amount emerges through rigorous application of percentage discount principles, specifically recognizing that sale prices represent residual percentages of original values rather than serving as bases for discount calculations themselves. This problem reinforces critical consumer mathematics concepts with substantial real-world applicability: understanding that "20% off" means paying 80% of original price, establishing algebraic relationships between known and unknown values, distinguishing between percentage representations and their absolute dollar manifestations, and executing precise decimal operations without premature rounding. Mastery of these integrated competencies empowers informed purchasing decisions, guards against retail pricing misconceptions, and builds foundational skills transferable to interest calculations, tax computations, and proportional reasoning across financial literacy domains. The solution pathway exemplifies how seemingly simple percentage problems require careful interpretation of referent quantities a conceptual hurdle many learners encounter until explicitly addressing the directional nature of percentage relationships.