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

Correct answer:

x =  24 cm

Step-by-step explanation:

h=3.6 m cm=3.6 100  cm=360 cm  h = n x h = (n+3)(x4)  h = (h/x+3) (x4)  h x=(h+3 x) (x4)  360 x=(360+3 x) (x4) 3x2+12x+1440=0 3x212x1440=0 3 ...  prime number 12=223 1440=25325 GCD(3,12,1440)=3  x24x480=0  a=1;b=4;c=480 D=b24ac=4241(480)=1936 D>0  x1,2=2ab±D=24±1936 x1,2=24±44 x1,2=2±22 x1=24 x2=20  x=x1=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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