Dear sir/ ma'am,
for an excursion, $12900 is collected from a group of students such that the same amount of money was contributed by each student. had there been 14 students more, each of them would have contributed $21 less. how much money is contributed by each student?
answer this as soon as possible as i have a test tomorrow.

$150

Step-by-step explanation:

Let n = the number of students and

Let x = the contribution per student.

We have two conditions:

(1)  12 900 = nx

(2) 12 900 = (n+14)(x - 21)

Set (1) = (2)                                   nx = (n+14)(x - 21)

Remove parentheses:                nx = nx - 21n + 14 x - 294

Subtract nx from each side         0 = -21n + 14x  - 294

Divide each side by -7            (3) 0 =     3n   -    2x +  42  

Divide each side of (1) by x     (4) n = 12 900/x

Substitute (4) into (3)                    0 = (3 × 12 900)/x - 2x + 42

                                                      0 = 38 700/x - 2x  + 42

Multiply each side by x                0 = 38 700     - 2x² + 42x

Multiply each side by -1                0 =  2x² - 42x - 38 700

Solve the quadratic equation  

x = [-b±√(b² - 4ac)]/(2a)

x = {42 ± √[(42² - 4×2(-38700)]}/(2 × 2)

  = [42 ± √(1764 +309 600]/4

  = [42 ± √(311 364)]/4

  = (42 ± 558)/4

  = 600/4

  = 150

Each student contributes $150.