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Define the variable.

Computer Science

ScanSolve AI Answer

Answer

45\text{45}

Step-by-step solution

4 steps

Here's how to solve the problem:

  1. Define the variable.

    Let xx be the number of students in the class.

  2. Formulate the equation.

    According to the problem, each student contributed as many rupees as the number of students. So, each student contributed xx rupees.
    The total amount collected is the product of the number of students and the contribution per student:

    Total amount=x×x=x2\text{Total amount} = x \times x = x^2

    We are given that the total amount collected is ₹2025.

    x2=2025x^2 = 2025

  3. Solve for xx.

    To find the number of students, we need to calculate the square root of 2025.

    x=2025x = \sqrt{2025}

    We can find the square root by prime factorization:

    2025=5×4052025 = 5 \times 405 405=5×81405 = 5 \times 81 81=9×9=9281 = 9 \times 9 = 9^2

    So,

    2025=5×5×9×9=52×92=(5×9)2=4522025 = 5 \times 5 \times 9 \times 9 = 5^2 \times 9^2 = (5 \times 9)^2 = 45^2

    Therefore,

    x=452x = \sqrt{45^2} x=45x = 45

  4. State the conclusion.

    The number of students in the class is 45.

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