Middle school math problems

Analysis: (1) because the use of recycling and purification equipment after 1 to x months (1 ≤ x ≤ 12) of the monthly average of the profit w (million yuan) to meet the w = 10x + 90, so y = xw = x (10x + 90);

Require the sum of the profits of the previous months = 7 million yuan, you can make y = 700, the use of equations can solve the problem;

(2) because The original monthly profit of 1.2 million yuan, the use of recycling and purification equipment after the 1 to x months of profit and not installing recycling and purification equipment x months of profit and equal, so there is

y = 120x, the solution to the answer;

(3) because the use of recycling and purification equipment after the first two years of profit = 12 x (10 x 12 + 90), and find the sum of them can be The

Solution: solution: (1) y=xw=x(10x+90)=10x2+90x,

10x2+90x=700,

Solve: x=5

Answer: the sum of the profits of the first five months is equal to 7 million yuan

(2) 10x2+90x=120x,

Solve: x=3

Answer: when x is 3, the sum of profits for months 1 through x after the use of the recycling and purification equipment is equal to the sum of profits for x months without the recycling and purification equipment.

(3) 12(10×12+90)+12(10×12+90)=50.4 million yuan.