To assemble a car, Leonid needed to buy several screws and dowels. When he approached the cash register, it turned out that the store was running a promotional offer, offering customers either a $15\%$ discount on the entire purchase or a $50\%$ discount on dowels. It turned out that the cost of the purchase with the discount did not depend on the chosen discount option. How much money did Leonid initially plan to spend on dowels, if he planned to spend 7 rubles on screws?

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According to the condition, $15\%$ of the total purchase cost constitutes $50\%$ of the cost of the dowels. Therefore, the cost of the dowels is $30\%$ of the total purchase cost. Consequently, the (planned) costs of the screws and dowels are in the ratio of $7:3$.

## Answer

3 rubles.

Does there exist such an $x$ that $\sqrt{x+9}+\sqrt{x}+\sqrt{x-9}=7$?

## Solution

The left side of the equation makes sense for $x \geq 9$. Therefore, $\sqrt{x} \geq 3, \sqrt{x+9} \geq \sqrt{9+9}=3\sqrt{2}$. Thus, $\sqrt{x+9}+\sqrt{x}+\sqrt{x-9} \geq 3\sqrt{2}+3 > 3 \cdot 3.14 = 7.2 > 7$.

## Answer

No such $x$ exists.