1. (15 points) In a bookstore, there is a rule for "summing" discounts: "if different types of discounts apply to an item, they are applied sequentially one after another." For example, if two discounts A% and B% apply to an item, the first discount is applied to the original price, and the second discount is applied to the result of the first discount. Currently, two discounts are in effect in the store: "Autumn" at $25 \%$ and "Random" - a non-zero discount of a whole number of percent, determined at the moment of purchase. Someone with a loyalty card, which gives a $20 \%$ discount on all items, bought a book for 69 rubles, the original price of which was 230 rubles. What was the size of the "Random" discount?
Answer: $50 \%$.

Solution. Note that the sequence of applying discounts is irrelevant, since applying a discount of A\% is equivalent to multiplying the cost of the item by ( $1-\frac{A}{100}$ ). Let $R$ be the magnitude of the "random" discount. Then, as a result of "summing" the three discounts, we get

$$
230 \cdot\left(1-\frac{25}{100}\right) \cdot\left(1-\frac{20}{100}\right) \cdot\left(1-\frac{R}{100}\right)=69 \Longleftrightarrow R=50
$$