Question

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?

Answer 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

Answer 2

How did you get - 0.2 from?

Answer 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
etc