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 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.

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.

We need to find the number of sophomores when the ratio of freshmen:sophomores:juniors is 4:5:3 and there are 72 total members. First, find the total parts in the ratio: 4 + 5 + 3 = 12 parts. Each part represents 72 ÷ 12 = 6 students. Since sophomores make up 5 parts of the ratio, there are 5 × 6 = 30 sophomores. A common mistake is dividing 72 by just one part of the ratio instead of the sum of all parts. Always add all ratio parts first to find what one part represents.

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.

When you encounter ratio problems involving total amounts, you need to find the actual quantities from the given ratio, then calculate based on those specific numbers.

Given the ratio $$7:3$$ for adult to student tickets, this means for every 7 adult tickets sold, 3 student tickets were sold. To find the actual numbers from 200 total tickets, think of this as $$7x + 3x = 200$$, where $$x$$ is the multiplier. This gives us $$10x = 200$$, so $$x = 20$$.

Therefore: Adult tickets = $$7 \times 20 = 140$$ and Student tickets = $$3 \times 20 = 60$$.

Now calculate revenue: Adult revenue = $$140 \times \12 = \1{,}680$$ and Student revenue = $$60 \times \8 = \480$$. Total revenue = $$\1{,}680 + \480 = \2{,}160$$, which is answer choice C.

Looking at the wrong answers: A) $$\1{,}920$$ likely comes from incorrectly calculating one of the ticket quantities or prices. B) $$\2{,}040$$ might result from mixing up the ratio (using $$3:7$$ instead of $$7:3$$) or making an arithmetic error. D) $$\2{,}240$$ could come from assuming all 200 tickets were sold at some average price without properly working through the ratio.

Strategy tip: In ratio problems, always convert the ratio to actual quantities first using the total given, then perform your calculations. Double-check that your individual quantities add up to the stated total before proceeding with further computations.

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 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.

When you encounter ratio problems, you're working with proportional relationships between quantities. The key is understanding that ratios tell you the relative amounts, not the actual amounts, until you're given one concrete value.

The ratio $$5:3$$ means that for every 5 apples, there are 3 oranges. Since you know there are 24 oranges, you can set up a proportion to find the number of apples. Think of this as: if 3 parts equal 24 oranges, then 5 parts equal how many apples?

First, find what one "part" represents: $$24 \div 3 = 8$$. So each part in the ratio equals 8 fruits. Since apples represent 5 parts, multiply: $$5 \times 8 = 40$$ apples.

You can verify this by checking that $$\frac{40}{24} = \frac{5}{3}$$, which simplifies correctly.

Looking at the wrong answers: A) 32 represents a calculation error where someone might have multiplied $$4 \times 8$$ instead of $$5 \times 8$$. B) 36 could result from incorrectly thinking the ratio is $$3:2$$ instead of $$5:3$$, then calculating $$\frac{3}{2} \times 24 = 36$$. D) 42 might come from adding the ratio parts incorrectly or making an arithmetic mistake in the proportion.

The correct answer is C) 40.

Strategy tip: For ratio problems, always identify what one "part" equals by dividing the known quantity by its ratio number, then multiply by the unknown quantity's ratio number. Double-check by verifying the final ratio matches the original.

When you encounter ratio problems, you're working with proportional relationships where two quantities must maintain a constant relationship to each other. The key is setting up a proportion that relates the given information to what you're trying to find.

Here, the red-to-white ratio must be $$7:4$$, which means for every 7 parts red paint, you need 4 parts white paint. Since you have exactly 5 gallons of red paint, you can set up the proportion: $$\frac{7}{4} = \frac{5}{x}$$, where $$x$$ is the gallons of white paint needed.

Cross-multiplying: $$7x = 4 \times 5 = 20$$, so $$x = \frac{20}{7} = 2.857...$$ gallons. Rounding to one decimal place gives approximately 2.9 gallons.

Looking at the wrong answers: Choice A (1.6 gallons) likely comes from incorrectly setting up the proportion as $$\frac{4}{7} = \frac{5}{x}$$ and making calculation errors. Choice B (2.1 gallons) might result from using an incorrect ratio or arithmetic mistakes. Choice D (3.6 gallons) could come from confusing the setup entirely, perhaps thinking you need more white than the ratio actually requires.

The correct answer is C) 2.9 gallons.

Strategy tip: Always double-check ratio problems by substituting your answer back into the original ratio. Here, $$\frac{5}{2.9} \approx \frac{7}{4} = 1.75$$, confirming your answer maintains the required proportion. Write out your proportion clearly before solving to avoid setup errors.