Keep the base visible through successive percentages
A percentage is attached to a base. OpenStax expresses a percent proportion as an amount compared with its base, equal to the percent compared with 100. In a two-stage problem, the first calculation may change the base of the second. Underline phrases such as discounted price, original price or remaining balance before choosing a formula. Worked example: an item starts at $120. A 20% discount leaves 120 × 0.80 = $96. A 5% tax on the discounted price adds 96 × 0.05 = $4.80, giving $100.80. One compact calculation is 120 × 0.80 × 1.05. The percentage signs do not mean that 20 and 5 can simply be combined as a 15% reduction from the starting amount. That subtraction shortcut gives $102 because it effectively calculates the tax on $120 instead of $96. To see the difference, write each dollar amount separately. The correct tax base is $24 lower, so 5% of that $24, or $1.20, accounts for the discrepancy. This makes the error visible rather than merely labeling a different option incorrect. Reversing a percent change also needs the right base. If a price of $96 is the result of a 20% discount, the starting value solves 0.80 × original = 96, so it is $120. Adding 20% of $96 gives $115.20 and does not undo the change. These examples teach base selection; they do not claim that every tax or fee uses the same rules. The diagnostic supplies the required order and excludes other charges.
An $80 item is discounted by 25%. An 8% tax is then applied to the discounted price. There are no other charges. What is the final price?
- The discount leaves 80 × 0.75 = $60. Tax is 8% of that $60, or $4.80. The final price is $64.80. Applying the tax to the original $80 would use the wrong base; adding and subtracting the two percentages as though they act on the same amount is not equivalent.
Compare the other answer choices
This stops at the discounted price and omits the stated tax.
This adds $6.40, or 8% of the original price, rather than $4.80.
This taxes the original price and omits the discount.
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.
ASVAB SubtestsSolve Proportions and their Applications