The question asks for the number of sophomores in a club with a freshmen-to-sophomores-to-juniors ratio of 4:5:3 and a total of 72 students. Set up the proportion with total parts as 4 + 5 + 3 = 12, so sophomores represent 5/12 of the total. Calculate (5/12) × 72 = 5 × 6 = 30 sophomores. Verify by distributing: freshmen 4 × 6 = 24, juniors 3 × 6 = 18, and 24 + 30 + 18 = 72. A key error might be confusing the parts or dividing total by the wrong number, such as using only two categories. When dealing with multi-part ratios, sum all parts first to ensure accurate proportion setup.

The question asks how many grams of chocolate are in a trail mix bag with nuts:raisins:chocolate ratio 9:4:2 and 180 grams of nuts. Set up the proportion: nuts 9 parts = 180, one part = 180 ÷ 9 = 20, chocolate = 2 × 20 = 40 grams. Verify: raisins = 4 × 20 = 80, total 180 + 80 + 40 = 300. Errors might involve wrong part assignment. Always calculate from the known component and sum for total verification.

The question asks for the original price of an item on sale at 85% for $153. Set up the proportion: sale price = 85% of original, so original = 153 ÷ 0.85. Calculate 153 ÷ 0.85 = 180. Using fractions: 153 / (85/100) = 153 × (100/85) = 180. Verify: 85% of 180 = 0.85 × 180 = 153. A common error is calculating percentage increase instead of decrease. When dealing with percentages, express as decimals carefully and check by reapplying the percentage.

The question asks how many students walk to school in a class of 80 with walk-to-bus ratio 11:9. Set up the proportion with total parts 11 + 9 = 20, so walkers = (11/20) × 80 = 44. Verify: bus = (9/20) × 80 = 36, and 44 + 36 = 80. Solve via cross-multiplication: walkers / 80 = 11 / 20, yielding 44. Errors often arise from not summing parts or assuming equal groups. In two-category ratios, confirm the total matches by adding both groups after calculation.

The question asks for the model car's length in centimeters, given a 1:24 scale and actual length of 4.32 meters. Set up the proportion: model = actual / 24, first converting actual to cm: 4.32 m = 432 cm, so model = 432 ÷ 24 = 18 cm. Alternatively, scale ratio 1:24 means model cm = (432 cm) × (1/24) = 18. Note units: ensure conversion from meters to centimeters before applying scale. A common error is forgetting unit conversion, leading to mismatched results. Double-check units in scale problems to match the requested output.

The question asks for the total number of marbles in a jar with red:blue:green ratio 6:5:4 and 45 blue marbles. Set up the proportion where blue is 5 parts = 45, so one part = 45 ÷ 5 = 9, and total parts = 15, so total = 15 × 9 = 135. Verify: red 6 × 9 = 54, green 4 × 9 = 36, and 54 + 45 + 36 = 135. Common errors include adding ratios incorrectly or using the wrong part for division. Always calculate one part from the known quantity and multiply by total parts for accuracy.

The question asks for the total donations split in ratio 13:7 for Cause A to B, with A receiving $1,560. Set up the proportion: A is 13 parts = 1,560, one part = 1,560 ÷ 13 = 120, total parts = 20, total = 20 × 120 = 2,400. Verify: B = 7 × 120 = 840, total 1,560 + 840 = 2,400. Common errors include dividing by the wrong part. In splitting ratios, find per-part value from known and multiply by total parts.

The question asks for the length of Rectangle B, given similar rectangles where A has length 14 cm and width 9 cm, and B has width 15.3 cm. Set up the proportion using the similarity ratio from widths: 15.3 / 9 = 1.7. Apply to lengths: 14 × 1.7 = 23.8 cm. Cross-multiply if using ratios: (length B / 14) = (15.3 / 9), so length B = 14 × (15.3 / 9) = 23.8. A key error is using the wrong corresponding sides. When working with similar figures, match corresponding dimensions carefully before scaling.

The question asks for the actual distance in miles between two towns that are 3.75 inches apart on a map with a scale of 1 inch = 18 miles. Set up the proportion where distance = map inches × miles per inch, so actual = 3.75 × 18. Calculate 3 × 18 = 54 and 0.75 × 18 = 13.5, totaling 67.5 miles. Cross-multiply if using a ratio: (3.75 inches / 1 inch) = (d miles / 18 miles), yielding d = 67.5. Common errors include forgetting to multiply the fractional part or mixing units. Pay careful attention to decimal places in map measurements for precise scaling.

This question requires finding the amount of yellow paint in 4.8 liters of a mixture with a blue:yellow:white ratio of 5:3:2 by volume. Set up the proportion by noting the total parts are 5 + 3 + 2 = 10, so yellow is 3/10 of the mixture. Multiply 4.8 L by 3/10 to get 1.44 L of yellow paint. This scales the ratio to the total volume directly. A common error is misadding the parts or assigning the wrong fraction to yellow, leading to incorrect amounts. Emphasize checking that the sum of all component volumes equals the total mixture. For strategy, verify by calculating all parts and summing them to match the total given.