A class of 234234 students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Let's define:

- \( r \) as the number of rows, and
- \( s \) as the number of students in each row.

According to the problem, the number of students in each row is one less than three times the number of rows. Therefore, we have:

\[
s = 3r - 1
\]

We are also told that the total number of students is 234,234. Since the total number of students is the product of the number of rows and the number of students per row, we can write the equation:

\[
r \times s = 234234
\]

Substituting \( s = 3r - 1 \) into the equation, we get:

\[
r \times (3r - 1) = 234234
\]

Expanding the equation:

\[
3r^2 - r = 234234
\]

Rearranging it into a standard quadratic form:

\[
3r^2 - r - 234234 = 0
\]

Now we can solve this quadratic equation using the quadratic formula:

\[
r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Where \( a = 3 \), \( b = -1 \), and \( c = -234234 \). Substituting these values into the quadratic formula:

\[
r = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(-234234)}}{2(3)}
\]

\[
r = \frac{1 \pm \sqrt{1 + 2808408}}{6}
\]

\[
r = \frac{1 \pm \sqrt{2808409}}{6}
\]

Taking the square root of 2,808,409:

\[
r = \frac{1 \pm 1676}{6}
\]

Now we have two possible solutions:

\[
r = \frac{1 + 1676}{6} = \frac{1677}{6} = 279.5
\]

\[
r = \frac{1 - 1676}{6}

A class of 234234 students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Learn how to solve a quadratic equation problem where 234,234 students are arranged in rows such that the number of students in a row is one less than three times the number of rows. This detailed step-by-step solution involves key algebraic concepts and uses the quadratic formula to find the number of rows and students per row. Suitable for Grades 9-12.

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