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.
Question
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.
Solution
Let's denote the number of rows as 'r' and the number of students in each row as 's'.
According to the problem, the number of students in a row is one less than thrice the number of rows. This can be written as:
s = 3r - 1
Also, the total number of students is the product of the number of rows and the number of students in each row. This can be written as:
234234 = r * s
Substitute s from the first equation into the second equation:
234234 = r * (3r - 1)
Solving this quadratic equation will give us the number of rows 'r'. Once we have 'r', we can substitute it back into the first equation to get the number of students in each row 's'.
Let's solve the quadratic equation:
234234 = 3r^2 - r 3r^2 - r - 234234 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0. The solutions can be found using the quadratic formula r = [-b ± sqrt(b^2 - 4ac)] / (2a).
In this case, a = 3, b = -1, and c = -234234.
Substituting these values into the quadratic formula gives:
r = [1 ± sqrt((1)^2 - 43(-234234))] / (2*3) r = [1 ± sqrt(1 + 2802804)] / 6 r = [1 ± sqrt(2802805)] / 6
The square root of 2802805 is approximately 1674.26. Since the number of rows can't be negative, we discard the solution with the minus sign:
r = (1 + 1674.26) / 6 r = 1675.26 / 6 r = approximately 279.21
Since the number of rows must be a whole number, we round this to the nearest whole number, which is 279.
Substituting r = 279 into the first equation gives:
s = 3*279 - 1 s = 837 - 1 s = 836
So, there are approximately 279 rows and 836 students in each row.
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