Middle School Math Quiz: Multi Step Ratio And Percent Problems
20 questions · exam conditions
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Multi Step Ratio And Percent ProblemsQuestion 1 of 20

A restaurant automatically adds an 18% gratuity to parties of 6 or more. If a party of 8 people has a bill of $240 before the gratuity, and they decide to leave an additional $15 cash tip, what is the total percent tip based on the original bill?

24.25%
22.50%
21.75%
23.25%
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Middle School Math Quiz

Middle School Math Quiz: Multi Step Ratio And Percent Problems

Practice Multi Step Ratio And Percent Problems in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Multi Step Ratio And Percent Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A restaurant automatically adds an 18% gratuity to parties of 6 or more. If a party of 8 people has a bill of $240 before the gratuity, and they decide to leave an additional $15 cash tip, what is the total percent tip based on the original bill?

  1. 24.25% (correct answer)
  2. 22.50%
  3. 21.75%
  4. 23.25%
Explanation: The automatic gratuity is $240 \times 0.18 = $43.20. Total tip is $43.20 + $15.00 = $58.20. The percent tip is $\frac{58.20}{240} \times 100% = 24.25%$. Choice B results from calculating only 18% + additional tip percentage without considering the automatic gratuity amount. Choice C comes from calculation errors. Choice D results from rounding errors in intermediate steps.

Question 2

Simple interest is calculated using the formula I=PRTI = PRT, where PP is principal, RR is annual rate, and TT is time in years. If $500 is invested at 4.5% annual simple interest and grows to $556.25 total, how many months was the money invested?

  1. 36 months
  2. 30 months (correct answer)
  3. 42 months
  4. 33 months
Explanation: The interest earned is 556.25 - 500 = $56.25. Using I = PRT, this gives 56.25 = 500 x 0.045 x T, so T = 56.25 / (500 x 0.045) = 56.25/22.5 = 2.5 years, which is 30 months. Choice A, choice C, and choice D come from arithmetic slips or from using an incorrect rate or time conversion when solving for T.

Question 3

In science class, a student estimated the mass of a rock as 54 g. The actual mass was 50 g. What is the percent error? (Use percent error =∣estimate−actual∣actual×100%=\dfrac{|\text{estimate}-\text{actual}|}{\text{actual}}\times 100\%.)

  1. 8%8\% (correct answer)
  2. 4%4\%
  3. 7.4%7.4\%
  4. 10%10\%
Explanation: This problem tests multi-step problems with percents, specifically percent error calculation. Using the given formula: percent error = |estimate - actual|/actual × 100%, we get |54 - 50|/50 × 100% = 4/50 × 100% = 0.08 × 100% = 8%. The percent error is 8%. A common error would be using the estimate in the denominator (4/54 ≈ 7.4%) or forgetting the absolute value (though not relevant here since estimate > actual). Strategy: (1) identify estimate (54g) and actual (50g), (2) find absolute difference |54 - 50| = 4, (3) divide by actual value (4/50 = 0.08), (4) convert to percent (0.08 × 100% = 8%), (5) verify reasonableness (4g error on 50g base is 8%✓). Percent error always uses actual value as the reference.

Question 4

At a school fundraiser, a T-shirt costs 18.0018.00 and the sales tax is 8%8\%. If you also donate an extra 10%10\% of the taxed total to support the club, how much do you pay altogether?

  1. 20.2020.20
  2. 21.0621.06
  3. 21.3821.38 (correct answer)
  4. 20.3420.34
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8%8\% of 40=40×0.08=3.2040 = 40 \times 0.08 = 3.20), increasing by percent (add: 40+3.20=43.2040 + 3.20 = 43.20, or multiply: 40×1.08=43.2040 \times 1.08 = 43.20 directly), decreasing (subtract or multiply by complement: 25%25\% off 80=80×0.75=6080 = 80 \times 0.75 = 60). Multi-step: tax then tip (meal 4545, tax 7%7\%: 45×1.07=48.1545 \times 1.07 = 48.15, tip 20%20\% on total: 48.15×1.20≈57.7848.15 \times 1.20 \approx 57.78, or combined: 45×1.07×1.2045 \times 1.07 \times 1.20). Simple interest I=PrtI = P r t (principal ×\times rate ×\times time in years: 1000×0.05×2=1001000 \times 0.05 \times 2 = 100). Percent change: (new−old)/old×100%( \text{new} - \text{old} ) / \text{old} \times 100\% (200→250200 \to 250: 50/200=25%50 / 200 = 25\% increase). For example, an item costs 1818, with 8%8\% tax: 18×0.08=1.4418 \times 0.08 = 1.44 tax, total 18+1.44=19.4418 + 1.44 = 19.44; then add 10%10\% donation on total: 19.44×0.10=1.94419.44 \times 0.10 = 1.944, altogether 19.44+1.944=21.38419.44 + 1.944 = 21.384 or directly 18×1.08×1.10=21.38418 \times 1.08 \times 1.10 = 21.384, rounded to 21.3821.38. The correct calculation is to first apply the 8%8\% tax to 1818 getting 19.4419.44, then add 10%10\% of that as donation, totaling 21.3821.38. A common error is calculating the donation on the pre-tax amount instead of the taxed total, leading to 18×0.10=1.8018 \times 0.10 = 1.80, then 18+1.44+1.80=21.2418 + 1.44 + 1.80 = 21.24, which is incorrect. Strategy: (1) identify operations needed (tax: multiply by 1+rate1 + \text{rate}, tip: multiply by 1+rate1 + \text{rate} on appropriate base, interest: I=PrtI = P r t), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents (8%=0.088\% = 0.08, 20%=0.2020\% = 0.20), (4) multiply for efficiency (increase by 8%8\% then 20%20\%: ×1.08×1.20\times 1.08 \times 1.20 in one calculation), (5) verify reasonable (total with tax and tip should be ~30%30\% more than meal: 45→∼5845 \to \sim 58 reasonable✓). Common formulas: simple interest I=PrtI = P r t (interest = principal ×\times rate decimal ×\times years), percent change = (new−old)/old( \text{new} - \text{old} ) / \text{old} (positive: increase, negative: decrease), percent error = ∣estimate−actual∣/actual| \text{estimate} - \text{actual} | / \text{actual} (absolute difference over actual). Mistakes: percent as whole number (most common: ×8\times 8 not ×0.08\times 0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=PrI = P r without tt, or wrong denominator in percent change).

Question 5

A car dealership offers a 3.5% commission on sales. In January, a salesperson sold cars worth $180,000 and earned $6,300 in commission. In February, total sales increased by 25%, but the commission rate was reduced. If the salesperson earned $6,615 in February, what was the new commission rate?

  1. 3.15%
  2. 2.94% (correct answer)
  3. 2.85%
  4. 3.25%
Explanation: When you see commission problems with changing rates and sales amounts, you need to work systematically through each scenario to find the unknown rate. First, let's verify the January information. With sales of $180,000 and a 3.5% commission rate: $180,000×0.035=6,300180,000 \times 0.035 = 6,300 $. This matches the given commission, so we're on track. Next, calculate February's sales. A 25% increase means: 180,000 \times 1.25 = 225,000 . Now we can find the new commission rate. Since commission equals sales times rate, we have: 225,000 \times \text{rate} = 6,615 . Solving for the rate: \text{rate} = \frac{6,615}{225,000} = 0.0294 = 2.94% . Looking at the wrong answers: Choice A (3.15%) is too high—this would give a February commission of $7,087.50, much more than the actual $6,615. Choice C (2.85%) is too low—this would yield only $6,412.50 in commission. Choice D (3.25%) is also too high—this would result in $7,312.50 in commission. The correct answer is B (2.94%). Strategy tip: In multi-step percentage problems, always verify your intermediate calculations before moving to the next step. Here, confirming the January numbers helped ensure accuracy, and calculating February sales before finding the rate kept the solution organized and error-free.

Question 6

A real estate agent charges a 6% commission on home sales. Last month, she sold 3 homes for $320,000, $275,000, and $410,000 respectively. If she splits her commission equally with her broker, how much money did she personally earn last month?

  1. $31,200
  2. $60,300
  3. $28,750
  4. $30,150 (correct answer)
Explanation: When you see commission problems, you're working with percentages and multi-step calculations. The key is to organize your work: find the total sales, calculate the commission, then apply any splits or deductions. First, find the total value of homes sold: 320,000+275,000+410,000=1,005,000320,000 + 275,000 + 410,000 = 1,005,000. Next, calculate the 6% commission on this total: 1,005,000×0.06=60,3001,005,000 × 0.06 = 60,300. Since she splits this commission equally with her broker, divide by 2: 60,300÷2=30,15060,300 ÷ 2 = 30,150. So she personally earned $30,150. Looking at the wrong answers: Choice A (31,200)likelycomesfromincorrectlycalculating631,200) likely comes from incorrectly calculating 6% of the total sales—perhaps rounding errors or miscalculating the percentage. Choice B (60,300) is the total commission before splitting with the broker; this represents forgetting the final step of dividing by 2. Choice C ($28,750) might result from calculation errors in either the total sales amount or the percentage calculation, possibly confusing which operations to perform. The correct answer is D ($30,150). Remember this pattern for commission problems: total sales × commission rate = total commission, then apply any splits or deductions. Always read carefully to see if the person keeps the full commission or shares it. Many students forget that final step of splitting the commission, so double-check what the question asks for—total commission earned or the person's actual share.

Question 7

A fundraiser collects 520520 in donations. The website charges a 3%3\% processing fee, then the organizer pays a flat 55 transfer fee. How much money is left after both fees (rounded to the nearest cent)?

  1. 499.40499.40 (correct answer)
  2. 510.00510.00
  3. 500.60500.60
  4. 504.40504.40
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of 4040 = 40×0.08=3.2040 \times 0.08 = 3.20), increasing by percent (add: 40+3.20=43.2040 + 3.20 = 43.20, or multiply: 40×1.08=43.2040 \times 1.08 = 43.20 directly), decreasing (subtract or multiply by complement: 25% off 8080 = 80×0.75=6080 \times 0.75 = 60). Multi-step: fees (donations 520520, 3% fee: 520×0.97=504.40520 \times 0.97 = 504.40 after, then subtract 55: 504.40−5=499.40504.40 - 5 = 499.40). For this problem, 520520 minus 3% fee (520×0.03=15.60520 \times 0.03 = 15.60, 520−15.60=504.40520 - 15.60 = 504.40), then minus 55: 504.40−5=499.40504.40 - 5 = 499.40. A common error is subtracting fees in wrong order or using 3% as addition instead of deduction, or forgetting the flat fee. Strategy: (1) identify operations needed (percent fee: ×(1−rate)\times(1-\text{rate}), flat fee: subtract), (2) sequence properly (percent then flat), (3) use decimal form of percents (3% = 0.03), (4) calculate step-by-step, (5) verify reasonable (fees total about 20.6020.60, 520−20.60=499.40520 - 20.60 = 499.40 yes). Common formulas: percent error = ∣estimate−actual∣/actual×100%|\text{estimate} - \text{actual}| / \text{actual} \times 100\%; mistakes include wrong sequence or percent as whole number.

Question 8

At a restaurant, a meal costs $36.00. The tax is 7%7\%, and you leave a 20%20\% tip on the total after tax. What is the total amount you pay (rounded to the nearest cent)?​

  1. $46.22 (correct answer)
  2. $45.36
  3. $43.20
  4. $46.08
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of 40=40×0.08=40 = 40×0.08=3.20), increasing by percent (add: 40+40+3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25% off 80=80×0.75=80 = 80×0.75=60). Multi-step: tax then tip (meal $45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). For this problem, meal is $36 with 7% tax (36×1.07=38.52), then 20% tip on total (38.52×1.20=46.224, rounded to $46.22). A common error is tipping on pre-tax amount instead of post-tax (tip on 36: 7.20, tax 2.52, total 36+2.52+7.20=45.72, wrong), or adding percents directly (7%+20%=27%, 36×1.27=45.72, ignores compounding). Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base), (2) sequence properly (tax before tip usually), (3) use decimal form of percents (7%=0.07, 20%=0.20), (4) multiply for efficiency (×1.07×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be ~27% more, but compounded to about 28.4%, 36→36→46.22 reasonable). Common formulas: percent change = (new-old)/old×100%; mistakes include wrong base for sequential percents or order wrong.

Question 9

A fundraiser collects $520 in donations. The website charges a 3%3\% processing fee, then the organizer pays a flat $5 transfer fee. How much money is left after both fees (rounded to the nearest cent)?

  1. $504.40
  2. $499.40 (correct answer)
  3. $500.60
  4. $510.00
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of 40=40×0.08=40 = 40×0.08=3.20), increasing by percent (add: 40+40+3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25% off 80=80×0.75=80 = 80×0.75=60). Multi-step: fees (donations $520, 3% fee: 520×0.97=504.40 after, then subtract $5: 504.40-5=499.40). For this problem, $520 minus 3% fee (520×0.03=15.60, 520-15.60=504.40), then minus 5:504.40−5=5: 504.40-5=499.40. A common error is subtracting fees in wrong order or using 3% as addition instead of deduction, or forgetting the flat fee. Strategy: (1) identify operations needed (percent fee: ×(1-rate), flat fee: subtract), (2) sequence properly (percent then flat), (3) use decimal form of percents (3%=0.03), (4) calculate step-by-step, (5) verify reasonable (fees total about $20.60, $520-20.60=20.60=499.40 yes). Common formulas: percent error = |estimate-actual|/actual×100%; mistakes include wrong sequence or percent as whole number.

Question 10

A family's restaurant bill (before tax) is $36.00. The sales tax is 7%7\%, and they leave a 20%20\% tip on the total after tax. What is the final amount they pay (rounded to the nearest cent)?

  1. $43.20
  2. $44.22
  3. $46.22 (correct answer)
  4. $45.36
Explanation: This problem tests multi-step problems with percents, requiring calculation of tax then tip on the after-tax total. First, we calculate the bill with tax: $36.00 × 1.07 = $38.52. Then we calculate the tip on this total: $38.52 × 1.20 = $46.224, which rounds to $46.22. Alternatively, we can combine the multipliers: $36.00 × 1.07 × 1.20 = $46.224. The correct calculation gives us 46.22.Acommonerrorwouldbecalculatingtiponthepre−taxamount(46.22. A common error would be calculating tip on the pre-tax amount (36 × 0.20 = $7.20) then adding both tax and tip to the original, which would give a different result. Strategy: (1) apply tax first to get after-tax total, (2) calculate tip on the after-tax amount as specified, (3) use decimal forms (7% = 0.07, 20% = 0.20), (4) multiply efficiently using 1.07 and 1.20, (5) verify reasonableness (roughly 30% more than original: 36→ 36 → ~47 is reasonable✓).

Question 11

A video game costs $50 before tax. The tax rate is 8%8\%. You have a coupon for 10%10\% off the pre-tax price, and the cashier applies the coupon first, then adds tax. What is the final price (rounded to the nearest cent)?

  1. $45.00
  2. $49.00
  3. $54.00
  4. $48.60 (correct answer)
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of 40=40×0.08=40 = 40×0.08=3.20), increasing by percent (add: 40+40+3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25% off 80=80×0.75=80 = 80×0.75=60). Multi-step: coupon then tax (game $50, 10% off: 50×0.90=45, then 8% tax: 45×1.08=48.60). For this problem, apply 10% coupon first: 50×0.90=45, then 8% tax: 45×1.08=48.60. A common error is applying tax before coupon (50×1.08=54, then 54×0.90=48.60 same here, but wrong if order specified), or discounting the tax amount. Strategy: (1) identify operations needed (discount: ×0.90, tax: ×1.08), (2) sequence properly (coupon before tax as stated), (3) use decimal form of percents, (4) multiply for efficiency (50×0.90×1.08=48.60), (5) verify reasonable (10% off saves $5, tax on $45 adds $3.60, total $48.60 yes). Common formulas: percent change = (new-old)/old×100%; mistakes include wrong order or adding percents directly.

Question 12

A science class estimated that a plant grew to 1818 cm, but the actual height was 1616 cm. What is the percent error? (Round to the nearest tenth of a percent.)

  1. 11.1%11.1\%
  2. 6.3%6.3\%
  3. 2%2\%
  4. 12.5%12.5\% (correct answer)
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of 40=40×0.08=40 = 40×0.08=3.20), increasing by percent (add: 40+40+3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25% off 80=80×0.75=80 = 80×0.75=60). Multi-step: tax then tip (meal $45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). Simple interest I=Prt (principal×rate×time in years: 1000×0.05×2=1000×0.05×2=100). Percent change: (new-old)/old×100% (200→250: 50/200=25% increase). For example, estimate 20 cm, actual 18 cm: |20-18|/18×100%≈11.1%, but note formula uses actual in denominator. The correct calculation is |18-16|/16×100%=2/16×100%=12.5%. A common error is using estimate in denominator: |18-16|/18×100%≈11.1%, or forgetting absolute value and getting negative. Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base, interest: I=Prt), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents (8%=0.08, 20%=0.20), (4) multiply for efficiency (increase by 8% then 20%: ×1.08×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be ~30% more than meal: 45→ 45→~58 reasonable✓). Common formulas: simple interest I=Prt (interest = principal × rate decimal × years), percent change = (new-old)/old (positive: increase, negative: decrease), percent error = |estimate-actual|/actual (absolute difference over actual). Mistakes: percent as whole number (most common: ×8 not ×0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=Pr without t, or wrong denominator in percent change).

Question 13

A student sells coupon books for a club. The student earns a 6%6\% commission on total sales. If the student sold $250 worth of coupon books, how much commission did the student earn?

  1. $265
  2. $150
  3. $14
  4. $15 (correct answer)
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of 40=40×0.08=40 = 40×0.08=3.20), increasing by percent (add: 40+40+3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25% off 80=80×0.75=80 = 80×0.75=60). Multi-step: tax then tip (meal $45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). Simple interest I=Prt (principal×rate×time in years: 1000×0.05×2=1000×0.05×2=100). Percent change: (new-old)/old×100% (200→250: 50/200=25% increase). For example, 6% commission on $200 sales: 200×0.06=12. The correct calculation is 250×0.06=15. A common error is using 6 instead of 0.06, getting 250×6=1500, or adding to sales like 250+15=265. Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base, interest: I=Prt), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents (8%=0.08, 20%=0.20), (4) multiply for efficiency (increase by 8% then 20%: ×1.08×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be ~30% more than meal: 45→ 45→~58 reasonable✓). Common formulas: simple interest I=Prt (interest = principal × rate decimal × years), percent change = (new-old)/old (positive: increase, negative: decrease), percent error = |estimate-actual|/actual (absolute difference over actual). Mistakes: percent as whole number (most common: ×8 not ×0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=Pr without t, or wrong denominator in percent change).

Question 14

A pair of sneakers is originally priced at $80. It is discounted by 15%15\%, and then an additional 10%10\% coupon is applied to the discounted price. What is the final price (rounded to the nearest cent)?

  1. $61.20 (correct answer)
  2. $64.80
  3. $68.00
  4. $60.00
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8%8\% of 40=40×0.08=3.2040 = 40 \times 0.08 = 3.20), increasing by percent (add: 40+3.20=43.2040 + 3.20 = 43.20, or multiply: 40×1.08=43.2040 \times 1.08 = 43.20 directly), decreasing (subtract or multiply by complement: 25%25\% off 80=80×0.75=6080 = 80 \times 0.75 = 60). Multi-step: successive discounts (item 8080, 15%15\% off: 80×0.85=6880 \times 0.85 = 68, then 10%10\% off: 68×0.90=61.2068 \times 0.90 = 61.20, or combined 80×0.85×0.90=61.2080 \times 0.85 \times 0.90 = 61.20). For this problem, original 8080, 15%15\% discount to 80×0.85=6880 \times 0.85 = 68, then 10%10\% coupon to 68×0.90=61.2068 \times 0.90 = 61.20. A common error is adding discounts directly (15%+10%=25%15\% + 10\% = 25\%, 80×0.75=6080 \times 0.75 = 60, wrong due to no compounding), or applying in wrong order. Strategy: (1) identify operations needed (discount: ×1\times 1-rate), (2) sequence properly, (3) use decimal form of percents (15%=0.1515\% = 0.15, 10%=0.1010\% = 0.10), (4) multiply for efficiency (×0.85×0.90=0.765\times 0.85 \times 0.90 = 0.765 overall, 80×0.765=61.2080 \times 0.765 = 61.20), (5) verify reasonable (total discount about 23.5%23.5\%, 80→61.2080 \rightarrow 61.20 yes). Common formulas: percent change = new−oldold×100%\frac{\text{new} - \text{old}}{\text{old}} \times 100\%; mistakes include adding percents directly or wrong base for sequential percents.

Question 15

A video game originally costs $60. It is discounted by 25%25\%, and then an additional 8%8\% sales tax is added to the discounted price. What is the final price (rounded to the nearest cent)?

  1. $48.60 (correct answer)
  2. $43.20
  3. $50.00
  4. $45.00
Explanation: This problem tests multi-step problems with percents, applying a discount followed by sales tax. First, we calculate the discounted price: $60 × 0.75 = $45 (25% off means paying 75%). Then we add 8% tax to the discounted price: $45 × 1.08 = $48.60. We can combine operations: $60 × 0.75 × 1.08 = $48.60. The final price is $48.60. A common error would be to calculate both percentages on the original price separately (25% of $60 = $15 discount, 8% of $60 = $4.80 tax) then compute $60 - $15 + $4.80 = $49.80, which incorrectly applies tax to the original rather than discounted price. Strategy: (1) apply discount first (multiply by 0.75 for 25% off), (2) then apply tax to the discounted amount (multiply by 1.08), (3) use complement for discounts (25% off = 75% of price), (4) sequence operations properly, (5) verify reasonableness (should be less than original $60 but not by full 25% due to tax✓).

Question 16

Maria's monthly salary increased from $3,200 to $3,680. Her boss told her this was a 12% raise, but Maria thinks it's more than 12%. What is the actual percent increase in Maria's salary, and is her boss correct?

  1. 15% increase; her boss is incorrect (correct answer)
  2. 12% increase; her boss is correct
  3. 13.6% increase; her boss is incorrect
  4. 14.2% increase; her boss is incorrect
Explanation: The actual increase is $3,680 - $3,200 = $480. The percent increase is $\frac{480}{3200} \times 100% = 15%.Herbossisincorrect.ChoiceBwouldbecorrectiftheincreasewereactually$384.ChoiceCresultsfromcalculating$4803680×100%. Her boss is incorrect. Choice B would be correct if the increase were actually $384. Choice C results from calculating $\frac{480}{3680} \times 100\% (using new salary as base). Choice D comes from estimation errors in the division.

Question 17

The enrollment at Jefferson Middle School decreased from 850 students to 765 students over two years. The school lost the same percentage of its current enrollment each year (not the same percentage of the original 850). What was the annual percent decrease?

  1. 4.76%
  2. 10%
  3. 5% (correct answer)
  4. 5.25%
Explanation: Let r be the annual decrease rate. After one year, enrollment is 850(1-r). After two years, it is 850(1-r)^2=765. Solving: (1-r)^2=765/850=0.9, so 1-r=the square root of 0.9, about 0.95, giving r=0.05=5%, matching choice C. Check: 850 x 0.95 x 0.95 is about 765.6, close to 765. Choice A (4.76%) would leave about 773 students, too high. Choice B (10%) is far too large, leaving only about 688 students. Choice D (5.25%) would leave about 763 students, close but not exact.

Question 18

A laptop originally priced at $1,200 is marked down 25% for a clearance sale. If the sales tax rate is 8.5%, what is the total amount a customer pays for the laptop during the clearance sale?

  1. $956.25
  2. $900.00
  3. $1,023.00
  4. $976.50 (correct answer)
Explanation: When you encounter multi-step percent problems involving discounts and taxes, work through them systematically: first apply the discount to find the sale price, then calculate tax on that discounted amount. Start with the 25% markdown. The laptop costs 1,200×0.25=$3001,200 \times 0.25 = \$300 less, so the sale price is 1,200−300=$9001,200 - 300 = \$900. Now apply the 8.5% sales tax to this discounted price: 900×0.085=$76.50900 \times 0.085 = \$76.50 in tax. The total amount paid is 900+76.50=$976.50900 + 76.50 = \$976.50. Looking at the wrong answers: Choice A (956.25)representsacommonerrorwherestudentssubtractthetaxfromthesalepriceinsteadofaddingit(956.25) represents a common error where students subtract the tax from the sale price instead of adding it ( 900−76.50900 - 76.50 ).ChoiceB(). Choice B (900.00) is just the sale price before tax—students who choose this forget to include sales tax entirely. Choice C ($1,023.00) comes from incorrectly applying the 8.5% tax to the original $1,200 price instead of the discounted price, then subtracting the $300 discount afterward. The correct sequence gives you D ($976.50). Study tip: Always remember the order matters in discount and tax problems. Discounts come first, then taxes are calculated on the already-reduced price. Sales tax is never applied to the original price when there's a discount involved. Write out each step clearly to avoid mixing up the sequence.

Question 19

A store marks up a jacket by 45% from its wholesale cost. During a sale, the store offers a 20% discount on the marked price. If the final sale price is $87, what was the wholesale cost of the jacket?

  1. $75.00 (correct answer)
  2. $60.00
  3. $65.50
  4. $72.50
Explanation: Let the wholesale cost be xx. After a 45% markup, the marked price is 1.45x1.45x. After a 20% discount, the sale price is 0.80(1.45x)=1.16x=870.80(1.45x) = 1.16x = 87. Solving: x=87÷1.16=75x = 87 ÷ 1.16 = 75. Choice B (60)wouldresultifyouincorrectlycalculatedthecompoundeffectas2560) would result if you incorrectly calculated the compound effect as 25% (45% - 20%). Choice C (65.50) results from applying the discount to the wholesale cost instead of the marked price. Choice D ($72.50) comes from reversing the order of operations.

Question 20

A store offers a 10%10\% discount on a $50 backpack. After the discount, an additional 5%5\% fee is added to the discounted price for customization. What is the final price?

  1. $45.00
  2. $47.25 (correct answer)
  3. $47.50
  4. $52.50
Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of 4040 = 40×0.08=3.2040 \times 0.08 = 3.20), increasing by percent (add: 40+3.20=43.2040 + 3.20 = 43.20, or multiply: 40×1.08=43.2040 \times 1.08 = 43.20), decreasing (subtract or multiply by complement: 25% off 8080 = 80×0.75=6080 \times 0.75 = 60). Multi-step: tax then tip (meal 4545, tax 7%: 45×1.07=48.1545 \times 1.07 = 48.15, tip 20% on total: 48.15×1.20≈57.7848.15 \times 1.20 \approx 57.78, or combined: 45×1.07×1.2045 \times 1.07 \times 1.20). Simple interest I=Prt (principal×rate×time in years: 1000×0.05×2=1001000 \times 0.05 \times 2 = 100). Percent change: (new−old)/old×100%(new-old)/old \times 100\% (200→250: 50/200=25% increase). For example, 5050 item, 10% discount: 50×0.90=4550 \times 0.90 = 45, then 5% fee: 45×1.05=47.2545 \times 1.05 = 47.25. The correct calculation is 50×0.90=45 discounted, then 45×1.05=47.25 final. A common error is adding the fee before discount, like 50×1.05=52.50, then 52.50×0.90=47.25 (same here, but wrong sequence could differ in other cases). Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base, interest: I=Prt), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents (8%=0.08, 20%=0.20), (4) multiply for efficiency (increase by 8% then 20%: ×1.08×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be 30% more than meal: 4545→$58 reasonable✓). Common formulas: simple interest I=Prt (interest = principal × rate decimal × years), percent change = (new-old)/old (positive: increase, negative: decrease), percent error = |estimate-actual|/actual (absolute difference over actual). Mistakes: percent as whole number (most common: ×8 not ×0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=Pr without t, or wrong denominator in percent change).