For any enzyme that follows simple Michaelis-Menten kinetics, when the initial Velocity of the reaction is 80% of Vmax what is the substrate concentration?

The answer is: [S] = 4Km

Can you explain why it is?

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  1. v = (VmaxS)/(K + S)
    when v = 0.8Vmax, then
    0.8Vmax = (VmaxS)/(K + S)
    0.8VmaxK + 0.8VmaxS = VmaxS
    0.8VmaxS - VmaxS = -0.8VmaxK
    -0.2VmaxS = -0.8VmaxK
    0.2VmaxS = 0.8VmaxK
    S = 0.8VmaxK/0.2Vmax
    S= 4K

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  2. How did you get - 0.2 from?

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  3. This entire problem is not about chemistry. It's just an exercise in algebra.
    Step 5 is
    0.8VmaxS - VmaxS = -0.8VmaxK
    So 0.8VmaxS - 1.0VmaxS = -0.8VmaxK and
    -0.2VmaxS = -0.8VmaxK

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