A student is asked to solve the following word problem: 'A person has a collection of items. The number of items is divisible by 5. If they acquire 10 more items, they will have a total of less than 50 items. What is the maximum possible original number of items in the collection?' The student's reasoning is outlined below. Identify the step that contains the first logical error.
- Let 'x' be the original number of items. The first condition states that 'x' must be a multiple of 5 (e.g., 5, 10, 15, 20, 25, 30, 35, 40, 45, ...).
- The second condition states that if 10 items are added, the total is less than 50. This can be written as the inequality: x + 10 < 50.
- To find the maximum possible value for 'x', we should first find the maximum value for the total (x + 10). Since the total must be less than 50, the maximum integer value the total can be is 50.
- Based on the previous step, we set up the equation x + 10 = 50. Solving for x gives us x = 40. Since 40 is divisible by 5, this is the maximum original number of items.
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Ch.5 Inference - Foundations of Large Language Models
Foundations of Large Language Models
Computing Sciences
Foundations of Large Language Models Course
Evaluation in Bloom's Taxonomy
Cognitive Psychology
Psychology
Social Science
Empirical Science
Science
Related
Concept of a Multiple of 5 (Jessica's Apps Problem)
Formulating the Inequality for the Total Number of Apps (Jessica's Apps Problem)
A student is asked to solve the following word problem: 'A person has a collection of items. The number of items is divisible by 5. If they acquire 10 more items, they will have a total of less than 50 items. What is the maximum possible original number of items in the collection?' The student's reasoning is outlined below. Identify the step that contains the first logical error.
- Let 'x' be the original number of items. The first condition states that 'x' must be a multiple of 5 (e.g., 5, 10, 15, 20, 25, 30, 35, 40, 45, ...).
- The second condition states that if 10 items are added, the total is less than 50. This can be written as the inequality: x + 10 < 50.
- To find the maximum possible value for 'x', we should first find the maximum value for the total (x + 10). Since the total must be less than 50, the maximum integer value the total can be is 50.
- Based on the previous step, we set up the equation x + 10 = 50. Solving for x gives us x = 40. Since 40 is divisible by 5, this is the maximum original number of items.
Applying Multi-Step Mathematical Reasoning
A student is solving the following word problem: 'The number of items in a collection is a multiple of 5. If 10 more items are added, the total will be less than 50. What is the maximum possible original number of items?' Arrange the following logical steps into the correct sequence to find the solution.