=10*(1+2+... +x) + 90x
=10*x(x+1)/2 + 90x
=5x^2 + 95x
Let 5x^2 + 95x = 700, and solve for x = -19/2 + 1/2*sqrt(921) ≈ 5.674, i.e., the sum of the profits for the first 5.674 months is $7 million (what a strange result).
(2) Let 5x^2 + 95x = 120x, and solve for x = 5. So the sum of profits from January to May after using the recycling and purification equipment is equal to the sum of profits for 5 months without the recycling and purification equipment.
(3) When x>12, i.e., from the second year onwards the monthly average of profits w = 10*12 + 90 = 2.1 million yuan, so the sum of profits in the two years after the use of recycling and purification equipment is
5*12^2 + 95*12 + 210*12 = 43.8 million yuan.