This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as determining how many students passed an exam. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as calculating a discount on a jacket purchase. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as calculating the amount used for supplies from a fundraiser. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as calculating a discount on a backpack. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as calculating a discount on a pair of shoes. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as calculating a discount on a book. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as calculating a discount on a tablet. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

When you encounter percentage problems involving multiple groups, work backwards from the final number to find the total. This question tests your ability to handle "percentages of percentages."

Let's set up the relationships step by step. If we call the total number of students $$x$$, then 35% of students bought cookies, which equals $$0.35x$$ students. Of those cookie buyers, 40% also bought lemonade. So the number who bought both items is $$0.40 \times 0.35x = 0.14x$$.

Since we know that 84 students bought both cookies and lemonade, we can write: $$0.14x = 84$$. Solving for $$x$$: $$x = 84 ÷ 0.14 = 600$$.

Let's verify: If 600 students participated, then $$600 \times 0.35 = 210$$ bought cookies, and $$210 \times 0.40 = 84$$ bought both items. ✓

Looking at the wrong answers: Choice B (700) would give us $$700 \times 0.14 = 98$$ students buying both items, not 84. Choice C (540) would result in $$540 \times 0.14 = 75.6$$ students, which is too low. Choice D (420) would give us $$420 \times 0.14 = 58.8$$ students, also too low.

The correct answer is A (600).

Strategy tip: In nested percentage problems, multiply the percentages together to find what fraction of the total the final group represents. Here, $$35% \times 40% = 14%$$ of all students bought both items.

This is a classic percentage problem where you know the percentage and the actual number, but need to find the total. When you see this type of question, set up the relationship: part = percentage × whole.

Here, 24% of the total equals 156 people. Let's call the total number of people surveyed $$x$$. So we have: $$0.24x = 156$$

To solve for $$x$$, divide both sides by 0.24: $$x = \frac{156}{0.24} = 650$$

You can verify this: 24% of 650 = 0.24 × 650 = 156 ✓

Now let's see why the other answers are wrong. Choice B (780) would mean 24% × 780 = 187.2 people, which is too many. Choice C (520) gives us 24% × 520 = 124.8 people, which is too few. Choice D (624) results in 24% × 624 = 149.76 people, also too few.

The correct answer is A (650).

Strategy tip: When solving "what is the total" percentage problems, remember the formula: Total = Part ÷ Percentage (as a decimal). Also, always check your answer by multiplying back: does your total × the given percentage equal the given part? This quick verification can catch calculation errors and boost your confidence.

This problem tests proportional reasoning and percentage calculations, which are fundamental skills in ratio and proportion problems. When you see a recipe problem asking for a different quantity, you need to scale all ingredients proportionally.

First, determine how many muffins Janet wants to make: 60% of 16 muffins equals $$0.60 \times 16 = 9.6$$ muffins. Since you can't make partial muffins in practice, this represents making 60% of the original batch.

Now set up a proportion to find the flour needed. If 2.5 cups makes 16 muffins, then $$x$$ cups makes 9.6 muffins:

$$\frac{2.5 \text{ cups}}{16 \text{ muffins}} = \frac{x \text{ cups}}{9.6 \text{ muffins}}$$

Cross multiply: $$2.5 \times 9.6 = 16x$$, so $$24 = 16x$$, which gives $$x = 1.5$$ cups.

Alternatively, since Janet is making 60% as many muffins, she needs 60% as much flour: $$0.60 \times 2.5 = 1.5$$ cups.

Looking at the wrong answers: Choice B (1.8) might result from incorrectly calculating 60% of something other than 2.5, or from computational errors. Choice C (2.0) could come from mistakenly thinking 60% means reducing by 0.5 cups. Choice D (1.2) might result from calculating 60% - 40% = 20% off the original, then subtracting incorrectly.

Strategy tip: In proportion problems, always check if you can solve more directly. Here, "60% as many muffins" means you need "60% as much of each ingredient" – sometimes the shortcut is clearer than setting up the full proportion.