Automaker

The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year?

Result

x =  10

Solution:

360=d⋅x 360=(d+4)⋅(x−1)  d=4x−4  x(4x−4)=360 4x2−4x−360=0  a=4;b=−4;c=−360 D=b2−4ac=42−4⋅4⋅(−360)=5776 D>0  x1,2=−b±D2a=4±57768 x1,2=4±768 x1,2=0.5±9.5 x1=10 x2=−9   Factored form of the equation:  4(x−10)(x+9)=0  x>0 x=10 d=4x−4=410−4=36360 = d \cdot x \ \\ 360 = (d+4) \cdot (x-1) \ \\ \ \\ d = 4 x - 4 \ \\ \ \\ x(4 x - 4) = 360 \ \\ 4x^2 -4x -360 =0 \ \\ \ \\ a=4; b=-4; c=-360 \ \\ D = b^2 - 4ac = 4^2 - 4\cdot 4 \cdot (-360) = 5776 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 4 \pm \sqrt{ 5776 } }{ 8 } \ \\ x_{1,2} = \dfrac{ 4 \pm 76 }{ 8 } \ \\ x_{1,2} = 0.5 \pm 9.5 \ \\ x_{1} = 10 \ \\ x_{2} = -9 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 4 (x -10) (x +9) = 0 \ \\ \ \\ x>0 \ \\ x = 10 \ \\ d = 4 x - 4 = 4 10 - 4 = 36

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