1. The price of a mathematics book in bookstore A at the beginning of January 2012 was higher than the price of the same book in bookstore B. On February 15, 2012, the price of the book in bookstore A decreased by $30\%$, while the price of the same book in bookstore B increased by $30\%$. Then, on March 15, 2012, the price of the book in bookstore A increased by $30\%$, and the price of the book in bookstore B decreased by $30\%$. The difference in the prices of the book after the changes on March 15, 2012, was 273 denars. By how much was the price of the mathematics book in bookstore A higher than the price of the same book in bookstore B at the beginning of January 2012?
Solution. Let the price of the book in bookstore A at the beginning of January 2012 be $x$, and the price of the same book in bookstore B be $y$. If the price $z$ is reduced by $30\%$, the new price will be $z-30\% z=z-0.3 z=0.7 z$, while if the price $z$ is increased by $30\%$, the new price will be $z+30\% z=1.3 z$.

|  | January 1 | February 15 | March 15 |
| :---: | :---: | :---: | :---: |
| bookstore A | $x$ | $0.7 \cdot x$ | $1.3 \cdot 0.7 \cdot x=0.91 \cdot x$ |
| bookstore B | $y$ | $1.3 \cdot y$ | $0.7 \cdot 1.3 \cdot x=0.91 \cdot x$ |

Given that $x>y$, therefore

$$
\begin{aligned}
& 0.91 x-0.91 y=0.91(x-y)=273 \\
& x-y=\frac{273}{0.91}=300
\end{aligned}
$$

The price of the mathematics book in bookstore A, at the beginning of January 2012, was higher than the price of the same book in bookstore B by 300 denars.