5. In a furniture store, work desks with one, two, and three drawers are sold. There are a total of 25 drawers in all the desks combined, and the number of desks with one drawer is equal to the number of desks with two and three drawers combined. Determine how many of each type of desk there can be.

Each task is scored out of 10 points.

The use of pocket calculators or any reference materials is not allowed.

## COUNTY COMPETITION IN MATHEMATICS
First method:

Let $a$ be the number of tables with one drawer, $b$ be the number of tables with two drawers, and $c$ be the number of tables with three drawers.

Then we have:

$a+2 b+3 c=25$

$a=b+c$

2 POINTS

$a, b, c \in \mathbb{N}$

By rearranging, we get the expression $3 b+4 c=25$.

2 POINTS

| $b, b \leq 8$ | $4 c=25-3 b$ | $c \in \mathbb{N}$ | $a=b+c$ | Solution $(a, b, c)$ |
| :---: | :---: | :---: | :---: | :---: |
| 1 | 22 | - | - |  |
| 2 | 19 | - | - |  |
| 3 | 16 | 4 | 7 | $(7,3,4)$ |
| 4 | 13 | - | - |  |
| 5 | 10 | - | - |  |
| 6 | 7 | - | - | 2 POINTS |
| 7 | 4 | - | - |  |
| 8 | 1 | 2 POINTS |  |  |
| 2 POINTS |  |  | - |  |

It can be: $\quad 7$ tables with one drawer, 3 tables with two drawers, and 4 tables with three drawers

or: $\quad 8$ tables with one drawer, 7 tables with two drawers, and 1 table with three drawers.

TOTAL 10 POINTS