Please help me with the quadratic equation problem!
A manufacturing crew needs to assemble 1000 boxes per day, divided equally among the workers. One day three workers call in sick, and the remaining members each need to assemble 75 more boxes than usual. How many workers are on the manufacturing crew?

Question

Please help me with the quadratic equation problem! 
A manufacturing crew needs to assemble 1000 boxes per day, divided equally among the workers. One day three workers call in sick, and the remaining members each need to assemble 75 more boxes than usual. How many workers are on the manufacturing crew?

anonymous · Answer

N= number workers
b = boxes per worker

N b = 1000  and
(N-3)(b+75) = 1000
so 
Nb +75 N -3b - 225 = 1000
1000 + 75N - 3b = 1225
75N-3b = 225
multiply by N
75 N^2 -3Nb -225N =0
75 N^2 -225 N -3000=0

N = [225 +- sqrt(225^2 + (4)(75)(3000)]/150

N = [225 +-  975]/150 = 8    ignore negative result

Nb = 1000 
b = 1000/8 = 125

(8-3)(125+75) = 5(200) =1000    checks