The question asks how many milliliters of acid should be added to 255 mL of water to maintain an acid-to-water ratio of 3:17. Set up the proportion where water is 17 parts corresponding to 255 mL, so find the value of one part: 255 ÷ 17 = 15 mL per part. Then, for acid, multiply by its parts: 3 × 15 = 45 mL. This keeps the ratio exact with total mixture of 20 parts. Common errors include reversing the ratio or forgetting to find the per-part value before scaling. Always verify units are consistent, like mL for both components. A useful strategy is to check if the final ratio matches the original after adding the amounts.

The question asks how many sophomores are in a class of 72 students with a freshmen-to-sophomores-to-juniors ratio of 4:5:3. Set up the proportion with total parts: 4 + 5 + 3 = 12 parts for 72 students, so one part = 72 ÷ 12 = 6 students. For sophomores, multiply by their parts: 5 × 6 = 30. This distributes the total correctly according to the ratio. A common error is forgetting to sum the parts or assigning the wrong part to a group. Ensure units (students) are consistent across the proportion. For strategy, after calculating, add up all groups to verify they total 72.

The question asks for the length of a model car in centimeters, scaled 1:18 from an actual 4.32 meters long. Set up the proportion: model = actual / 18 = 4.32 / 18 = 0.24 meters. Convert to centimeters: 0.24 * 100 = 24 cm. Alternatively, convert actual to cm first: 4.32 * 100 = 432 cm, then 432 / 18 = 24 cm. Avoid errors like multiplying instead of dividing by the scale factor, which would inflate the size. Carefully handle unit conversions from meters to centimeters. For tests, confirm the scale direction (model to actual) before calculating.

The question asks how many sophomores are in a club with a 4:5:3 ratio of freshmen to sophomores to juniors and 48 total students. Set up the proportion by finding total parts: 4 + 5 + 3 = 12 parts, where sophomores are 5 parts. Sophomores = (5/12) * 48 = 20. Scale by dividing 48 by 12 to get 4 per part, then 5 * 4 = 20. Avoid the error of dividing total by one ratio only, which ignores the full proportion. Units are counts of students, so no conversion needed. For tests, check if the sum of all groups equals the total after calculation.

The question asks how many kilograms of flour are needed to match 1.8 kilograms of sugar in a 7:3 flour-to-sugar ratio. Set up the proportion where flour/sugar = 7/3, so flour = (7/3) * sugar = (7/3) * 1.8. Calculate 7 * 1.8 = 12.6, then divide by 3 to get 4.2 kilograms. This maintains the ratio by scaling the flour accordingly. A common mistake is inverting the ratio, like using 3/7, which would give an incorrect smaller amount. Always note the units, here kilograms for both ingredients. For tests, verify by checking if the total mixture follows the original ratio when combined.

This percentage problem asks how many students chose option A if 35% of 280 students made this choice. To find 35% of 280, multiply: 0.35 × 280 = 98 students. You can also think of this as (35/100) × 280 = 9800/100 = 98. A common mistake is forgetting to convert the percentage to a decimal or fraction before multiplying. When working with percentages, always convert to decimal form (divide by 100) before calculating.

The question asks what percent the straight-line map distance is of the actual driving distance, given a scale of 1 inch to 30 miles, map distance 2.75 inches, and driving distance 96 miles. Set up the proportion for actual straight-line distance: 2.75 × 30 = 82.5 miles. Then, find the percentage: (82.5 / 96) × 100 ≈ 85.9375%, which rounds to 86%. Calculate carefully and round to the nearest whole percent as instructed. Errors can occur in forgetting to multiply by the scale or misrounding. Ensure units match when comparing distances. A strategy is to estimate: 2.75 × 30 is about 82.5, and 82.5/96 is roughly 86%.

The question asks for the length of the side in triangle DEF corresponding to AC in similar triangle ABC, where AB=9 cm, AC=12 cm, and DE=15 cm corresponds to AB. Set up the proportion using the scale factor from ABC to DEF as DE/AB = 15/9 = 5/3. Apply this to AC: corresponding side = (5/3) * 12 = 20 cm. This ensures similarity by scaling all sides equally. A key error is mismatching corresponding sides, leading to wrong proportions. Confirm units are consistent, here all in centimeters. As a strategy, list corresponding sides clearly before setting up ratios.

The question asks how many liters of white paint are needed for 9 liters of gray paint mixed in the ratio of blue to white to black as 5:8:2. Set up the proportion by finding the total parts in the ratio, which is 5 + 8 + 2 = 15 parts, where white paint represents 8 parts. The amount of white paint is then (8/15) of the total 9 liters, so calculate (8/15) * 9 = 72/15 = 4.8 liters. This setup ensures the ratio remains consistent by scaling all components equally. A key error to avoid is forgetting to find the total parts, which might lead to incorrectly dividing by just one ratio value. Always double-check units to confirm they match, here all in liters. As a test-taking strategy, verify the answer by checking if all parts sum to the total volume when scaled.

With a scale of 1:24 (model:actual), we need to find the actual car length when the model is 18.5 cm. The scale means 1 unit on the model represents 24 units on the actual car. Therefore, actual length = model length × 24 = 18.5 × 24 = 444 cm. Students often confuse scale ratios and divide instead of multiply, or use the ratio backwards. Remember: when the scale is model:actual and you have the model size, multiply by the second number to get actual size.