13.076. The collection of corn from the fields of a livestock farm was 4340 centners. The following year, it is planned to obtain 5520 centners of corn by increasing the area by 14 hectares and increasing the yield by 5 centners per hectare. Determine the area occupied by corn and the yield in centners per hectare (the yield was less than 40 centners per hectare).
Solution.

Let $x$ ha be the area occupied by corn, $\frac{4340}{x}$ centners/ha the yield. The next year, the area is $x+14$ ha, and the yield is $\frac{4340}{x}+5$ centners/ha. According to the condition, $\left(\frac{4340}{x}+5\right)(x+14)=5520$, from which $x=98$ ha or $x=124$ ha. The yield is $\frac{4340}{98} \approx 44.3$ centners/ha or $\frac{4340}{124}=35$ centners/ha.

Answer: 124 ha; 35 centners per ha.