Prove that it cannot be proven that "The United States had more fallow acreage than planted acreage" Followup question to Prove "If, in a country, there are $x$ fallow acres for every planted acre, yield per planted acre is $1+x$ times the yield per total acre."
Given:

A ten year comparison between the United States and the Soviet Union
  in terms of crop yields per acre revealed that when only planted
  acreage is compared, Soviet yields were equal to 68 percent of United
  States yields. When total agricultural acreage (planted acreage plus
  fallow acreage) is compared, however, Soviet yield was 114 percent of
  US yield. From the information above, show that it cannot be proven that The United States had more fallow acreage than planted acreage.

 A: Let $p_u,f_u$ be the planted/fallow acreage in the U.S. and $p_s,f_s$ be the planted/fallow acreage in the Soviet Union. Also, let $y_u$ be the yield per planted acre in the U.S. and $y_s$ be the yield per planted acre in the Soviet Union. The information given says that
$$\frac{y_s}{y_u} = 0.68 \; \iff \; y_s = 0.68y_u \tag{1}\label{eq1}$$
The crop amount in the U.S. is $y_u p_u$, so the yield per the total acreage would be
$$y_{tu} = \frac{y_u p_u}{p_u + f_u} \tag{2}\label{eq2}$$
Similarly, for the Soviet Union, it's yield per the total acreage used would be
$$y_{ts} = \frac{y_s p_s}{p_s + f_s} \tag{3}\label{eq3}$$
By cross-multiplying and combining the terms for $f_s$ and $p_s$, you get
\begin{align}
y_{ts}(p_s + f_s) & = y_s p_s \\
y_{ts}p_s + y_{as}f_s & = y_s p_s \\
y_{ts}f_s & = y_s p_s - y_{ts}p_s \\
f_s & = \frac{p_s(y_s - y_{ts})}{y_{ts}} \tag{4}\label{eq4}
\end{align}
It's also given that
$$\frac{y_{ts}}{y_{tu}} = 1.14 \; \iff \; y_{ts} = 1.14y_{tu} \tag{5}\label{eq5}$$
I originally misread the question to think it was asking to show it cannot be proven whether the fallow or the planted U.S. acreage was larger. However, the answer to the actual question just needs to show that $f_u \le p_u$ is possible, which is done with the second set of calculations. For the more general question this originally answered, note this is the only information provided, so it can be answered if $2$ sets of values are found which are consistent with the above equations but with one showing that $f_u \gt p_u$ and the other showing that $f_u \lt p_u$.
Let's set $y_u = 100$. Then from \eqref{eq1}, you get $y_s = 68$. Next, let $p_u = 10,000,000$ and $f_u = 11,000,000$. Substituting these into \eqref{eq2} gives $y_{tu} = 47.619\ldots$. From \eqref{eq5}, this gives $y_{ts} = 54.285\ldots$. From \eqref{eq4}, you get
$$f_s = \frac{p_s(68 - 54.285\ldots)}{54.285\ldots} \tag{6}\label{eq6}$$
Note you can plug any value of $p_s$ you want to get a specific value of $f_s$, e.g., if $p_s = 10,000,000$, then $f_s = 2,526,315.789\ldots$.
Next, consider $f_u = 9,000,000$. Then \eqref{eq2} gives $y_{tu} = 52.631\ldots$. From \eqref{eq5}, this gives $y_{ts} = 60$. From \eqref{eq4}, you get
$$f_s = \frac{p_s(68 - 60)}{60} \tag{7}\label{eq7}$$
If you use $p_s = 10,000,000$ again, then $f_s = 1,333,333.333\ldots$.
All of these values are consistent with the equations relating the only information which was provided, but with one set showing more fallow acreage than planted acreage in the U.S. (i.e., $f_u = 11,000,000 \gt p_u = 10,000,000$) and the other one showing the opposite (i.e., $f_u = 9,000,000 \lt p_u = 10,000,000$).
A main reason why you can't prove which of the fallow and planted acreage in the U.S. is greater is because there are $6$ input values of $p_u,f_u,p_s,f_s,y_u$ and $y_s$, but only $4$ equations of \eqref{eq1}, \eqref{eq2}, \eqref{eq3} and \eqref{eq5} using them to relate to specified constants and other variables. Note, however, these $6$ input values are not independent of each other, with some being simply defined in terms of others, such as $y_s$ in terms of $y_u$ in \eqref{eq1}. In particular, as these equations are consistent with each other, it's an under-determined system of equations, with $6 - 4 = 2$ degrees of freedom in this case (in general, you would have more than $2$ if any of the equations are linearly dependent). Also, note the question's numeric value restrictions are for comparing values between the U.S. and the Soviet Union, meaning there are fewer constraints among the values within the U.S. (and the Soviet Union as well).
