13.060. A load with a mass of 60 kg presses on a support. If the mass of the load is reduced by 10 kg, and the area of the support is reduced by 5 dm², then the mass per square decimeter of the support will increase by 1 kg. Determine the area of the support.
Solution.

Let $x$ dm $^{2}$ be the area of the support. Then $\frac{60}{x}$ kg/dm² is the mass per 1 dm ${ }^{2}$ of the support. After reducing the mass of the load and the area of the support, this mass is $\frac{50}{x-5}$ kg/dm². According to the condition, $\frac{50}{x-5}-1=\frac{60}{x}$, from which $x=15$.

Answer: 15 dm $^{2}$.