This question tests middle school proportional reasoning skills, specifically solving scaling problems using ratios. Proportional reasoning involves understanding and applying the constant relationship between quantities, often expressed as ratios or fractions. In this problem, the scenario requires calculating the new dimensions of a poster enlarged by a factor of 2. The correct answer, choice A, accurately reflects the proportional relationship and demonstrates correct application of scaling procedures, as 14 × 2 = 28 and 10 × 2 = 20 cm. Choice D is incorrect because it represents a common error, such as multiplying by 10 instead of 2. To support students, emphasize understanding ratio relationships and practicing with real-world examples, such as adjusting recipes or map reading. Encourage checking calculations for unit consistency and logical accuracy.

This question tests middle school proportional reasoning skills, specifically solving scaling problems using ratios. Proportional reasoning involves understanding and applying the constant relationship between quantities, often expressed as ratios or fractions. In this problem, the scenario requires calculating the original length of a bridge from a 45 cm model at 1:100 scale. The correct answer, choice B, accurately reflects the proportional relationship and demonstrates correct application of scaling procedures, as 45 × 100 = 4500 cm or 45 m. Choice A is incorrect because it represents a common error, such as forgetting to convert units or apply the full scale. To support students, emphasize understanding ratio relationships and practicing with real-world examples, such as adjusting recipes or map reading. Encourage checking calculations for unit consistency and logical accuracy.

This question tests middle school proportional reasoning skills, specifically solving scaling problems using ratios. Proportional reasoning involves understanding and applying the constant relationship between quantities, often expressed as ratios or fractions. In this problem, the scenario requires calculating the new dimensions of a sketch enlarged by a factor of 4/3. The correct answer, choice A, accurately reflects the proportional relationship and demonstrates correct application of scaling procedures, as 9 × (4/3) = 12 and 6 × (4/3) = 8 cm. Choice D is incorrect because it represents a common error, such as multiplying by 4 instead of 4/3. To support students, emphasize understanding ratio relationships and practicing with real-world examples, such as adjusting recipes or map reading. Encourage checking calculations for unit consistency and logical accuracy.

This question tests middle school proportional reasoning skills, specifically solving scaling problems using ratios. Proportional reasoning involves understanding and applying the constant relationship between quantities, often expressed as ratios or fractions. In this problem, the scenario requires calculating the actual distance between two towns using the map scale of 1 inch = 6 miles and a map distance of 3.5 inches. The correct answer, choice A, accurately reflects the proportional relationship and demonstrates correct application of scaling procedures, as 3.5 × 6 = 21 miles. Choice B is incorrect because it represents a common error, such as dividing instead of multiplying by the scale factor. To support students, emphasize understanding ratio relationships and practicing with real-world examples, such as adjusting recipes or map reading. Encourage checking calculations for unit consistency and logical accuracy.

This question tests middle school proportional reasoning skills, specifically solving scaling problems using ratios. Proportional reasoning involves understanding and applying the constant relationship between quantities, often expressed as ratios or fractions. In this problem, the scenario requires calculating the actual length of a bike route using the map scale of 1 inch = 2.5 miles and a map length of 4.2 inches. The correct answer, choice C, accurately reflects the proportional relationship and demonstrates correct application of scaling procedures, as 4.2 × 2.5 = 10.5 miles. Choice D is incorrect because it represents a common error, such as multiplying by 4 instead of 2.5. To support students, emphasize understanding ratio relationships and practicing with real-world examples, such as adjusting recipes or map reading. Encourage checking calculations for unit consistency and logical accuracy.

This question tests middle school proportional reasoning skills, specifically solving scaling problems using ratios. Proportional reasoning involves understanding and applying the constant relationship between quantities, often expressed as ratios or fractions. In this problem, the scenario requires calculating the original height of a rocket from a 20 cm model at 1:30 scale. The correct answer, choice A, accurately reflects the proportional relationship and demonstrates correct application of scaling procedures, as 20 × 30 = 600 cm or 6 m. Choice C is incorrect because it represents a common error, such as inverting the scale or misconverting units. To support students, emphasize understanding ratio relationships and practicing with real-world examples, such as adjusting recipes or map reading. Encourage checking calculations for unit consistency and logical accuracy.

Scale problems require you to set up proportions carefully, paying close attention to units. When you see a scale like 1:48, this means 1 unit on the model equals 48 of those same units on the actual object.

First, convert the actual wingspan to inches since the answer choices are in inches: 36 feet × 12 inches/foot = 432 inches.

Now set up your proportion using the scale 1:48. If 1 inch on the model represents 48 inches on the actual airplane, then:

$$\frac{1 \text{ inch model}}{48 \text{ inches actual}} = \frac{x \text{ inches model}}{432 \text{ inches actual}}$$

Cross multiply: $$48x = 432$$, so $$x = 9$$ inches.

Looking at the wrong answers: Choice A (6 inches) might result from incorrectly dividing 36 by 6 instead of properly converting to inches first. Choice C (12 inches) could come from mistakenly thinking the scale means the model is 1/12 the size of the actual plane, confusing the 12 inches per foot conversion. Choice D (18 inches) might result from dividing the actual wingspan in feet (36) by some incorrect scale factor.

The correct answer is B (9 inches).

Study tip: In scale problems, always make sure your units match throughout your calculation. Convert everything to the same unit before setting up your proportion, and remember that a 1:48 scale means the model is 1/48 the size of the actual object.

This is a proportion problem where you need to scale a recipe up from serving 6 people to serving 14 people. When you see recipe scaling questions, set up a proportion to find the relationship between the original and new amounts.

Start by setting up the proportion: $$\frac{\text{original flour}}{\text{original people}} = \frac{\text{new flour}}{\text{new people}}$$

Substituting the known values: $$\frac{1.5 \text{ cups}}{6 \text{ people}} = \frac{x \text{ cups}}{14 \text{ people}}$$

Cross multiply to solve: $$1.5 \times 14 = 6 \times x$$, which gives you $$21 = 6x$$, so $$x = 3.5$$ cups.

You can also think of this as finding the flour needed per person first: $$1.5 ÷ 6 = 0.25$$ cups per person. Then multiply by 14 people: $$0.25 \times 14 = 3.5$$ cups.

Choice A (3.0 cups) is too small and likely comes from incorrectly doubling the original amount since 14 is roughly twice 6, but this ignores the exact proportional relationship. Choice C (4.0 cups) might result from rounding errors or miscalculating $$1.5 \times 14 ÷ 6$$. Choice D (4.5 cups) could come from adding instead of using proportional reasoning, perhaps thinking $$1.5 + 3 = 4.5$$.

For proportion problems on the SSAT, always set up your ratios carefully and double-check by working backwards—does 3.5 cups divided by 14 people equal 1.5 cups divided by 6 people? Both equal 0.25 cups per person, confirming your answer.

When you see a photograph enlargement problem, you're dealing with similar figures and proportional relationships. The key insight is that when a photograph is enlarged, both dimensions change by the same scale factor to maintain the same shape.

Start by identifying the scale factor. The original longer side is 6 inches, and it becomes 15 inches in the enlargement. So the scale factor is $$\frac{15}{6} = 2.5$$. This means every dimension of the photograph is multiplied by 2.5.

Now apply this scale factor to the shorter side: $$4 \times 2.5 = 10$$ inches. You can verify this makes sense by checking that the ratio of sides remains the same: originally $$\frac{6}{4} = 1.5$$, and in the enlargement $$\frac{15}{10} = 1.5$$.

Looking at the wrong answers: Choice (A) 9 inches would give a scale factor of $$\frac{9}{4} = 2.25$$, which doesn't match our scale factor of 2.5. Choice (C) 11 inches represents the trap of adding the same amount (9 inches) to the shorter side as was added to the longer side, but this doesn't preserve proportions. Choice (D) 12 inches might come from incorrectly doubling the original shorter side plus adding 4, but this also breaks the proportional relationship.

The correct answer is (B) 10 inches.

Strategy tip: In proportion problems, always find the scale factor first by comparing corresponding sides, then apply that same factor to find unknown dimensions. Cross-check by verifying the ratios remain equal.

This is a rate problem that tests your ability to find unit rates and use proportional reasoning. When you see a question giving you one rate and asking for a related quantity, think about finding the rate per unit first.

Start by finding the car's gas mileage (miles per gallon). Divide 280 miles by 8 gallons: $$280 ÷ 8 = 35$$ miles per gallon. Now you know the car travels 35 miles on each gallon of gas.

To find how many gallons are needed for 525 miles, divide the total distance by the miles per gallon: $$525 ÷ 35 = 15$$ gallons. You can verify this with a proportion: $$\frac{280 \text{ miles}}{8 \text{ gallons}} = \frac{525 \text{ miles}}{x \text{ gallons}}$$. Cross-multiplying gives $$280x = 525 \times 8 = 4200$$, so $$x = 15$$ gallons.

Looking at the wrong answers: Choice A (12 gallons) is too low and might result from incorrectly calculating the unit rate or making an arithmetic error. Choice B (13 gallons) is also too low and could come from rounding errors during calculation. Choice D (17 gallons) is too high and might result from using an incorrect proportion setup or calculation mistake.

The correct answer is C) 15 gallons.

Strategy tip: For rate problems, always find the unit rate first (like miles per gallon or cost per item). This makes the rest of the problem straightforward division or multiplication. Double-check by seeing if your answer makes sense—525 miles is less than double 280 miles, so the gas needed should be less than double 8 gallons.