Automaker

A car manufacturer now produces 4 more cars per day than last year, meaning 360 cars can be produced in one fewer working day. How many working days were needed to produce 360 vehicles in the previous year?

Final Answer:

x =  10

Step-by-step explanation:

$$\begin{gathered} 360=d\cdot x \\ 360=(d+4)\cdot (x-1) \\ d=4x-4 \\ x(4x-4)=360 \\ 4x^2-4x-360=0 \\ 4=2^2 \\ 360=2^3\cdot 3^2\cdot 5 \\ \text{GCD}(4,4,360)=2^2=4 \\ {x}^2-x-90=0 \\ a=1;b=-1;c=-90 \\ D=b^2-4ac=1^2-4\cdot 1\cdot (-90)=361 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{1\pm \sqrt{361}}{2} \\ {x}_{1,2}=\frac{1\pm 19}{2} \\ {x}_{1,2}=0.5\pm 9.5 \\ {x}_1=10 \\ {x}_2=-9 \\ \text{ Factored form of the equation: } \\ (x-10)(x+9)=0 \\ x>0 \\ x=10 \\ d=4x-4=410-4=36 \end{gathered}$$

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