Reverse a percentage change in the correct order
A percentage compares a part with a base. After a 20% reduction, the retained amount is 80% of the original base. Adding 20% of the reduced amount does not undo that reduction, because the two percentages use different bases. Translate the words into an equation before moving numbers. Worked example: a catalog fee is discounted 10%, then a fixed $4 mailing charge is added, producing a $31 total. Let the original fee be x. The relation is 0.90 x+4=31. Removing the fixed addition gives 0.90 x=27, then dividing by 0.90 gives x=30. Forward checking confirms 0.90×30+4=31. Dividing the entire 31 by 0.90 would incorrectly apply the discount relationship to mailing too. Write the order of operations in words beside the equation: change the base by a percentage, then add the fixed amount. Reverse those operations in the opposite order when solving. Do not decide on multiplication or division solely from the word percent. The diagnostic is an original fee problem with fully specified arithmetic, not a financial recommendation. Rounding is unnecessary for its exact values; when a different problem requires rounding, state the requested precision rather than silently changing the calculation.
An archive subscription has a base charge. A 20% discount is applied to that base, then a fixed $6 dispatch charge is added. The final total is $46. What was the base charge?
- Remove the undiscounted dispatch charge first: 46−6=40. The $40 is 80% of the base, so 0.8 x=40 and x=50. Checking forward gives 0.8×50+6=46.
Compare the other answer choices
Dividing 46 by 0.8 before subtracting 6 incorrectly treats the dispatch charge as discounted too.
Multiplying the discounted $40 by 0.8 applies another discount rather than finding the original base.
Adding 20% to the discounted $40 uses the reduced amount as the percentage base and does not reverse a 20% reduction.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Roy Simpson/LibreTexts—Percents