4. Let 2 cups and 2 pitchers weigh as much as 14 plates, 1 pitcher weighs as much as 1 cup and 1 plate. How many plates will balance a pitcher

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
4. First method of solution (graphical).

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-036.jpg?height=237&width=791&top_left_y=2052&top_left_x=632)

Reduce the number of items on each scale by half.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-037.jpg?height=231&width=786&top_left_y=244&top_left_x=635)

Now replace the jug on the left scale with a plate and a cup.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-037.jpg?height=157&width=780&top_left_y=635&top_left_x=638)

Remove a plate from each scale.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-037.jpg?height=160&width=780&top_left_y=882&top_left_x=635)

Reduce the number of items on each scale by half.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-037.jpg?height=154&width=782&top_left_y=1191&top_left_x=637)

Since one jug weighs as much as one cup and one plate, we get:

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-037.jpg?height=237&width=782&top_left_y=1503&top_left_x=637)

Second method of solution (analytical).

According to the problem, 2 cups + 2 jugs = 14 plates. Dividing both sides of the equation by 2, we get 1 cup + 1 jug = 7 plates. According to the second condition, 1 jug = 1 cup + 1 plate. From the subsequent two equations, we have:

$$
\begin{aligned}
& 1 \text{ cup } + 1 \text{ jug } = 7 \text{ plates; } \\
& 1 \text{ jug } = 1 \text{ cup } + 1 \text{ plate; } \\
& 1 \text{ cup } + 1 \text{ cup } + 1 \text{ plate } = 7 \text{ plates; } \\
& 2 \text{ cups } = 6 \text{ plates; } \\
& 1 \text{ cup } = 3 \text{ plates; } \\
& 1 \text{ jug } = 1 \text{ cup } + 1 \text{ plate } = 3 \text{ plates } + 1 \text{ plate } = 4 \text{ plates. }
\end{aligned}
$$

Third method of solution (arithmetic).

1) $14 \div 2 = 7$ (plates) - will balance 1 cup and 1 plate;
2) $7 - 1 = 6$ (plates) - will balance 2 cups;
3) $6 \div 2 = 3$ (plates) - will balance 1 cup;
4) $3 + 1 = 4$ (plates) - will balance 1 jug.

Answer: one jug balances 4 plates.