1. (15 points) Pavel caught 32 crayfish and decided to sell them at the market. When part of his catch was bought, it turned out that the buyer paid 4.5 rubles less for each one than the number of crayfish that remained on the counter. At the same time, the boy earned the maximum amount of money possible. How much money did Pavel earn? How many crayfish did he sell?
Solution: Let $x$ be the number of crayfish left on the counter, then (32-x) crayfish were bought, ($x-4.5$) - the cost of one crayfish.

$(32-x)(x-4.5)$ - the cost of all crayfish.

$y=(32-x)(x-4.5)$

$x_{B}=18.25$.

$x_{1}=19, y_{1}=(32-19)(19-4.5)=13 * 14.5=188.5$.

$x_{2}=18, y_{2}=(32-18)(18-4.5)=14 * 13.5=189$. The maximum number is 14.

Answer: a) the maximum amount of money is 189 rubles;

b) sold 14 crayfish.

| Points |  |
| :--- | :--- |
| 15 | The correct answer is obtained with justification. |
| 10 | An arithmetic error is made in an otherwise correct solution. |
| 5 | The problem is solved by trial and error, finding values of the variable that satisfy the condition. |
| 2 | There are some guesses. |
| 0 | The solution does not meet any of the criteria listed above. |