Problem solving & data analysis
⏱ ~3-min readAceMark Guide
What this topic is really about
Proportional relationships between quantities can be used to solve problems.. Because the recipe is linear, 3 cups for 12 cookies gives a rate of 3/12 = ¼ cup per cookie; multiplying ¼ by 20 cookies yields 5 cups.
The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles.. The total number of marbles in the jar is 20, so the probability of drawing a blue marble is the number of blue marbles over the total, or 8/20, which simplifies to 2/5.
See the mechanism
The total number of marbles in the jar is 20, and there are 8 blue marbles. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.
An exam-style question, fully explained
A jar contains 12 red and 8 blue marbles. Probability of drawing a blue marble:
- Identify what the question tests: A jar contains 12 red and 8 blue marbles..
- The total number of marbles in the jar is 20, so the probability of drawing a blue marble is the number of blue marbles over the total, or 8/20, which simplifies to 2/5.
- Option C is incorrect because 3/5 represents the probability of drawing a red marble, not a blue one.
- Why it matters: The total number of marbles in the jar is 20, and there are 8 blue marbles. To find the probability of drawing a blue marble, we divide the number of blue marbles by the total number of marbles, resulting in 8/20, which simplifies to 2/5. This fraction represents the chance of drawing a blue marble from the jar.
Traps the examiner sets
- People often get confused with the number of red marbles, which is 12, and mistakenly use it to calculate the probability of drawing a blue marble. However, the correct calculation is based on the number of blue marbles over the total number of marbles.
- People often get confused with percentages and decimal conversions, which can lead to incorrect calculations. In this case, ensuring that 15% is correctly converted to 0.15 is crucial for solving the equation accurately.
- Failing to adjust the proportion when scaling up the number of cookies, leading to underestimation of the required flour.
- Option C is incorrect because 3/5 represents the probability of drawing a red marble, not a blue one.
- Option D is incorrect because 15% of 150 is 22.5, which does not satisfy the given condition.
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