13.158. Apples of the 1st grade for a total of 228 rubles and apples of the 2nd grade for a total of 180 rubles were delivered to the store. During unloading, the delivered apples were accidentally mixed. It was found that if all the apples are now sold at one price - 90 kopecks lower than the price per kilogram of 1st grade apples, the previously planned amount will be earned. How many kilograms of apples were delivered, if it is known that there were 5 kg more of 2nd grade apples than 1st grade apples?
## Solution.

Let $x$ kg of apples of the first grade and $x+5$ kg of apples of the second grade be delivered to the store. In total, $2x+5$ kg of apples were delivered. A kilogram of apples of the 1st grade costs $\frac{228}{x}$ rubles. The new price of apples $-\left(\frac{228}{x}-0.9\right)$ rubles. The amount received from the sale of all apples $-\left(\frac{228}{x}-0.9\right)(2 x+5)$. According to the condition $\left(\frac{228}{x}-0.9\right)(2 x+5)=228+180$, from which $x=40$ kg. In total, $2 \cdot 40+5=85$ kg of apples were delivered.

Answer: 85 kg.