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Correct Answer: student a: 20%
mr. pyle has asked his students to calculate the percentage of students who will attend an after-school program in the library out of the total class. according to the problem statement, there are 25 students in the class, and 5 of those students will go to the library after school.
to solve this problem, we need to find what percentage of the total class the 5 students represent. this can be done using a simple proportion where the part (students attending the after-school program) is divided by the whole (total number of students), and then multiplied by 100 to convert the fraction into a percentage.
let's analyze each student's response:
- **student a** calculates the percentage as follows:
1. set up the proportion to find the percentage: \( \frac{5}{25} = \frac{x}{100} \)
2. cross multiply to solve for \( x \): \( 25x = 500 \)
3. solve for \( x \) by dividing both sides by 25: \( x = \frac{500}{25} = 20 \)
hence, student a concludes that 20% of the students will go to the library, which is the correct answer.
- **student b** suggests 25%, which is incorrect. this answer might result from a misunderstanding of the total number of students or a miscalculation.
- **student c** suggests 5%, which is also incorrect. this percentage represents a direct misinterpretation of the number of students going to the library as the percentage, ignoring the total class size in the calculation.
- **student d** suggests 30%, which is incorrect. this answer could come from adding the percentages of students picked up by parents and those riding the bus, then mistakenly including an additional percentage for the library attendees, which is not how percentages in this context are calculated.
in conclusion, **student a** provides the correct response by accurately calculating the percentage through setting up the correct proportion, cross-multiplying, and solving for the variable to find that 20% of the students attend the after-school program in the library. this method is a standard approach for solving percentage problems and reflects a good understanding of basic mathematical principles involving proportions.
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