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 $40$ = $40 \times 0.08 = 3.20$), increasing by percent (add: $40 + 3.20 = 43.20$, or multiply: $40 \times 1.08 = 43.20$ directly), decreasing (subtract or multiply by complement: 25% off $80$ = $80 \times 0.75 = 60$). Multi-step: fees (donations $520$, 3% fee: $520 \times 0.97 = 504.40$ after, then subtract $5$: $504.40 - 5 = 499.40$). For this problem, $520$ minus 3% fee ($520 \times 0.03 = 15.60$, $520 - 15.60 = 504.40$), then minus $5$: $504.40 - 5 = 499.40$. 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: $\times(1-\text{rate})$, 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 $20.60$, $520 - 20.60 = 499.40$ yes). Common formulas: percent error = $|\text{estimate} - \text{actual}| / \text{actual} \times 100%$; mistakes include wrong sequence or percent as whole number.

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 $40$ = $40 \times 0.08 = 3.20$), increasing by percent (add: $40 + 3.20 = 43.20$, or multiply: $40 \times 1.08 = 43.20$), decreasing (subtract or multiply by complement: 25% off $80$ = $80 \times 0.75 = 60$). Multi-step: tax then tip (meal $45$, tax 7%: $45 \times 1.07 = 48.15$, tip 20% on total: $48.15 \times 1.20 \approx 57.78$, or combined: $45 \times 1.07 \times 1.20$). Simple interest I=Prt (principal×rate×time in years: $1000 \times 0.05 \times 2 = 100$). Percent change: $(new-old)/old \times 100%$ (200→250: 50/200=25% increase). For example, $50$ item, 10% discount: $50 \times 0.90 = 45$, then 5% fee: $45 \times 1.05 = 47.25$. 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: $45$→$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).

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=$3.20), increasing by percent (add: $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=$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→$46.22 reasonable). Common formulas: percent change = (new-old)/old×100%; mistakes include wrong base for sequential percents or order wrong.

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=$3.20), increasing by percent (add: $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=$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→$46.22 reasonable). Common formulas: percent change = (new-old)/old×100%; mistakes include wrong base for sequential percents or order wrong.

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=$3.20), increasing by percent (add: $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=$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=$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=$499.40 yes). Common formulas: percent error = |estimate-actual|/actual×100%; mistakes include wrong sequence or percent as whole number.

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.

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. 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 → ~$47 is reasonable✓).

This problem tests multi-step problems with percents, specifically simple interest calculation using the formula I = Prt. We have principal P = $400, rate r = 0.05 (5% as decimal), and time t = 3 years: I = $400 × 0.05 × 3 = $60. The interest earned is $60. A common error would be forgetting to multiply by time (calculating just $400 × 0.05 = $20 for one year) or using the percent as a whole number ($400 × 5 × 3 = $6,000). Strategy: (1) identify the three components: principal ($400), rate (5% = 0.05), time (3 years), (2) apply formula I = Prt, (3) ensure rate is in decimal form, (4) multiply all three values, (5) verify reasonableness (5% per year for 3 years = 15% total of $400 = $60✓). Simple interest accumulates linearly, not compounded.

This problem tests multi-step problems with percents, applying a discount followed by sales tax. First, we calculate the discounted price: $8.00 \times 0.85 = 6.80$ (15% off means paying 85%). Then we add 8% tax to the discounted price: $6.80 \times 1.08 = 7.344$, which rounds to $7.34$. We can combine: $8.00 \times 0.85 \times 1.08 = 7.344$. The final price is $7.34$. A common error would be to subtract then add the same percentage thinking they cancel ($8.00 \times 0.93 = 7.44$, incorrectly netting 15% - 8% = 7%) or applying both to the original price separately. Strategy: (1) apply discount first (multiply by 0.85), (2) then apply tax to discounted amount (multiply by 1.08), (3) round only at the end to avoid rounding errors, (4) remember operations are sequential not simultaneous, (5) verify result is reasonable (should be less than $8$ but not by full 15% due to tax✓).

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 $40 = 40 \times 0.08 = 3.20$), increasing by percent (add: $40 + 3.20 = 43.20$, or multiply: $40 \times 1.08 = 43.20$ directly), decreasing (subtract or multiply by complement: $25%$ off $80 = 80 \times 0.75 = 60$). Multi-step: tax then tip (meal $45$, tax $7%$: $45 \times 1.07 = 48.15$, tip $20%$ on total: $48.15 \times 1.20 \approx 57.78$, or combined: $45 \times 1.07 \times 1.20$). Simple interest $I = P r t$ (principal $\times$ rate $\times$ time in years: $1000 \times 0.05 \times 2 = 100$). Percent change: $( \text{new} - \text{old} ) / \text{old} \times 100%$ ($200 \to 250$: $50 / 200 = 25%$ increase). For example, an item costs $18$, with $8%$ tax: $18 \times 0.08 = 1.44$ tax, total $18 + 1.44 = 19.44$; then add $10%$ donation on total: $19.44 \times 0.10 = 1.944$, altogether $19.44 + 1.944 = 21.384$ or directly $18 \times 1.08 \times 1.10 = 21.384$, rounded to $21.38$. The correct calculation is to first apply the $8%$ tax to $18$ getting $19.44$, then add $10%$ of that as donation, totaling $21.38$. A common error is calculating the donation on the pre-tax amount instead of the taxed total, leading to $18 \times 0.10 = 1.80$, then $18 + 1.44 + 1.80 = 21.24$, which is incorrect. Strategy: (1) identify operations needed (tax: multiply by $1 + \text{rate}$, tip: multiply by $1 + \text{rate}$ on appropriate base, interest: $I = P r t$), (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 $20%$: $\times 1.08 \times 1.20$ in one calculation), (5) verify reasonable (total with tax and tip should be ~$30%$ more than meal: $45 \to \sim 58$ reasonable✓). Common formulas: simple interest $I = P r t$ (interest = principal $\times$ rate decimal $\times$ years), percent change = $( \text{new} - \text{old} ) / \text{old}$ (positive: increase, negative: decrease), percent error = $| \text{estimate} - \text{actual} | / \text{actual}$ (absolute difference over actual). Mistakes: percent as whole number (most common: $\times 8$ not $\times 0.08$), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors ($I = P r$ without $t$, or wrong denominator in percent change).