Home › Certifications › 7th Math: Ratios & Proportional Relationships › Percent Problems: Discount, Tax, Markup, Interest
47 multiple-choice questions and 19 flashcards on Percent Problems: Discount, Tax, Markup, Interest, about 31% of the 7th Math: Ratios & Proportional Relationships bank. Every one carries a written rationale.
Percent Problems: Discount, Tax, Markup, Interest is one of 4 chapters in CoStudy's 7th Math: Ratios & Proportional Relationships bank, and it holds 47 of the bank's 150 multiple-choice questions — roughly 31% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
A real-world application of proportional reasoning is:
Answer: C — Scaling recipes, converting currencies, reading maps, computing taxes/tips/discounts, calculating speed/distance/time, comparing unit prices — proportional reasoning is used daily
Proportional reasoning is foundational to everyday math. (A), (B), (D) understate.
Mr. Lee earns 8% commission on his sales. To earn $400 in commission, his sales must total:
Answer: D — $5,000
D) 0.08 × sales = $400 → sales = $400/0.08 = $5,000. A) Multiplied. B) Used 80%. C) Misplaced decimal.
A $40 item is marked up 50% and then marked down 50%. The final price is:
Answer: A — $30
A) $40 × 1.50 = $60; $60 × 0.50 = $30. C) Common error: assuming percent changes cancel. B) Subtracted twice. D) Stopped at markup.
A shirt is marked down 25% from $40. The sale price is:
Answer: D — $30
D) Discount = 0.25 · 40 = $10; sale = $40 − $10 = $30. A) The discount only. B) Wrong subtraction. C) Added markup.
An item sells for $84 after a 30% markup over cost. The cost was:
Answer: C — $64.62
C) Cost × 1.30 = $84 → cost = $84/1.30 ≈ $64.62. A) Subtracted $30 from $84. B) Took 70% of $84. D) Added 33%.
A salesperson earns a base $300 plus 5% commission on $2,000 in sales. Total earnings:
Answer: C — $400
C) Commission = 0.05 × $2,000 = $100; total = $300 + $100 = $400. A) Commission only. B) Base only. D) Added all wrong amounts.
A jacket regularly $80 is on sale at 25% off, then an additional 10% off the sale price at checkout. Final price:
Answer: B — $54
B) $80 × 0.75 = $60; $60 × 0.90 = $54. A) Used 35% as a single discount. C) Stopped at 25% then subtracted $4. D) Stopped at 25% off.
A class survey shows 12 of 30 students prefer pizza. The probability a random student prefers pizza:
Answer: A — 40% (12/30)
12/30 = 0.4 = 40%. (B), (C), (D) miscalculate.
A car battery's voltage measured 11.4 V; the actual voltage is 12 V. The percent error is:
Answer: A — 5%
A) |11.4 − 12|/12 × 100% = 0.6/12 × 100% = 5%. B) Reported absolute error. C) Divided by 11.4. D) Misplaced decimal.
At a 1:3 mixing ratio of orange concentrate to water, how much water for 2 cups of concentrate?
Answer: C — 6 cups
1:3 × 2 = 2:6. So 6 cups of water. (A), (B), (D) miscalculate.
4 cards from the 19 in this chapter.
Calculate total bill on $35 with 18% tip.
$41.30.
A store buys an item for $40 and sells it for $60. Markup percent?
50%. (Markup $20 / cost $40 = 50%.)
Worked example: A $60 item is marked down 25%. Find the sale price.
Step 1 — Find the discount: discount = price × rate = $60 × 0.25. Step 2 — Compute: $60 × 0.25 = $15. Step 3 — Subtract: sale price = original − discount = $60 − $15. Step 4 — Result: sale price = $45. Step 5 — Shortcut check: original × (1 − rate) = $60 × 0.75 = $45. ✓
A $60 shirt is on sale for $45. What's the discount percent?
25%. (Discount $15 / original $60 = 0.25.)
These are a sample. The full Percent Problems: Discount, Tax, Markup, Interest chapter runs 66 items with per-chapter progress tracking, on the web and in the iOS app.
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