Answer:
$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.
