Staircase

On a staircase 3.6 meters high, the number of steps would increase by 3 if the height of one step decreased by 4 cm. How high are the stairs?

Correct result:

x =  24 cm

Solution:

h=3.6 m→ cm=3.6⋅ 100  cm=360 cm  h=n⋅ x h=(n+3)(x−4)  h=(h/x+3)⋅ (x−4)  h∗x=(h+3∗x)∗(x−4)  360⋅ x=(360+3⋅ x)⋅ (x−4) −3x2+12x+1440=0 3x2−12x−1440=0  a=3;b=−12;c=−1440 D=b2−4ac=122−4⋅3⋅(−1440)=17424 D>0  x1,2=−b±D2a=12±174246 x1,2=12±1326 x1,2=2±22 x1=24 x2=−20   Factored form of the equation:  3(x−24)(x+20)=0  x=x1=24=24 cm  n=h/x=360/24=15   Verifying Solution:  h1=n⋅ x=15⋅ 24=360 cm h2=(n+3)⋅ (x−4)=(15+3)⋅ (24−4)=360 cm

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