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)(x4)  h=(h/x+3) (x4)  hx=(h+3x)(x4)  360 x=(360+3 x) (x4) 3x2+12x+1440=0 3x212x1440=0  a=3;b=12;c=1440 D=b24ac=12243(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(x24)(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) (x4)=(15+3) (244)=360 cm

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