I am trying to establish possible points for a graded assignment in which I gave students a choice for the type of assessment. I want both of the assessment types to be worth the same amount of the final grade. For fairness, I will excuse the student from the option that they did not choose.
Let's establish some terms. Use K for Knowledge, which is 50% of the final grade. Use W for Writing, which is 15% of the final grade. Points possible for the assessment may be represented as P or a numerical value (20?).
If I determine the points possible for the W assessment as 20, how many points possible should the K assessment be worth?
Knowledge and Writing are in a ratio of $50:15$. Or, dividing by $15$, a ratio of $\tfrac{10}{3}:1$. Noting that K counts more, we know that this means that every $1$ point in K counts for $\frac{10}3$ in W (because the other way around wouldn't make sense). So to use the same units (those of W) the question is $x$ units of K $= \frac{10}{3}x$ units of W $= 20$ units of W. That is $$\frac{10}{3}x = 20.$$ To solve for $x$ we multiply both sides by the reciprocal, yielding $$x = \frac{3}{10}20 = 6.$$