This question is based on the storm caused by this twitter post. Since a twitter discussion is not an objective question, I'll simply write out the key elements of the problem.
Movie earning estimates were reported as roughly \$15 million in total revenue across about 2 million transactions where the rental option was \$6 and the sale purchase option was \$15 dollars.
Emphasizing that the given number of transactions and revenue are rough estimates, can this be solved algebraically? That is, can the two "rough" equations simply be solved to determine the two unknowns $r$ and $s$ (rentals and sales)? To be clear, $r$ and $s$ represent the number of transactions.
If solving these equations is valid, then what is the graphical explanation for why these two seemingly unrelated equations (one is number of transactions the other is revenue) can be solved?
If I'm understanding the scenario correctly, wouldn't it just be: $$ \begin{cases} r + s = 2 \;\mathrm{million} \\ 6r + 15s = 15 \;\mathrm{million} \end{cases} $$
To take the roughness of the equations into account, we can edit our constants to incorporate an error term: $$ \begin{cases} r + s = (2 \;\mathrm{million} \pm e_c) \\ 6r + 15s = (15 \;\mathrm{million} \pm e_r) \end{cases} $$ where $e_c$ is the "error in the count" and $e_r$ is the "error in the revenue." We can just solve these normally for $r$ and $s$ and see what happens to the error terms. Scratching it out, I get something like: $$ \begin{align} s = \frac{1}{3} \;\mathrm{million} \mp \frac{2}{3}e_c \pm \frac{1}{9}e_r \\ r = \frac{5}{3} \;\mathrm{million} \pm \frac{5}{3}e_c \mp \frac{1}{9}e_r \end{align} $$ This quantifies how much the error in the original equations propagates through to the values for $s$ and $r$. We see that any error in the estimation for the total count has much more influence over the values of $r$ and $s$ than errors in the revenue.