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This problem describes a recipe where the mass ratio of ingredients—dried meat, tomatoes, and cabbage—is 1:2:7. Let's solve the questions step by step:

### Given ratio: 
Dried meat : Tomatoes : Cabbage = 1 : 2 : 7

### a) How much tomatoes and cabbage are needed if there is 200 g of meat?

Let’s denote the mass of dried meat as \( x \). The mass of tomatoes would be \( 2x \), and the mass of cabbage would be \( 7x \).

If dried meat is 200 g, then:

- Tomatoes = \( 2 \times 200 = 400 \, \text{g} \)
- Cabbage = \( 7 \times 200 = 1400 \, \text{g} \)

Thus, with 200 g of meat, you need **400 g of tomatoes** and **1400 g of cabbage**.

### b) How much meat and cabbage are needed if there are 600 g of tomatoes?

Since the mass of tomatoes is \( 2x \), we can find \( x \) by solving:

\[ 2x = 600 \implies x = 300 \, \text{g} \]

Now, using this value of \( x \):

- Meat = \( x = 300 \, \text{g} \)
- Cabbage = \( 7x = 7 \times 300 = 2100 \, \text{g} \)

Thus, with 600 g of tomatoes, you need **300 g of meat** and **2100 g of cabbage**.

### c) How much of each ingredient is needed to make approximately 3 kg (3000 g) of stew?

The total ratio of ingredients is \( 1 + 2 + 7 = 10 \). So, the total mass of the ingredients must also follow this ratio.

Let’s denote the mass of all ingredients as \( 10x \), where \( 10x = 3000 \, \text{g} \). Solving for \( x \):

\[ 10x = 3000 \implies x = 300 \, \text{g} \]

Now we can calculate the mass of each ingredient:

- Meat = \( x = 300 \, \text{g} \)
- Tomatoes = \( 2x = 600 \, \text{g} \)
- Cabbage = \( 7x = 2100 \, \text{g} \)

Thus, for 3 kg of stew, you need **300 g of meat**, **600 g of tomatoes**, and **2100 g of cabbage**.

### d) Explain how you calculated each part.

- In part (a), the ratio of ingredients was used to scale the masses of tomatoes and cabbage according to the known mass of meat (200 g).
- In part (b), the known mass of tomatoes (600 g) was used to determine the other ingredients by first finding the mass of meat through the ratio.
- In part (c), the total desired mass of 3 kg was divided by the sum of the parts in the ratio (10) to determine how much each part should weigh. Then, each ingredient's mass was calculated using the given ratio.

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Would you like more details on any of these calculations or have additional questions?

Here are five questions you can explore further:
1. How would the recipe change if the ratio of tomatoes to cabbage was modified?
2. Can you calculate the mass of each ingredient for a total stew mass of 5 kg?
3. What would happen if the ratio of dried meat was doubled, but the total mass remained the same?
4. How can the recipe be adjusted if only 150 g of cabbage is available?
5. What would the new mass proportions be if the tomatoes and cabbage ratio was reversed?

**Tip:** When dealing with ratios, always sum the parts to determine how the total mass should be split!

Cik daudz tomātu un kāpostu nepieciešams, ja ir 200 g gaļas? Cik daudz gaļas un kāpostu nepieciešams, ja ir 600 g tomātu? Cik daudz katras sastāvdaļas nepieciešams, ja vēlas pagatavot apmēram 3 kg sautējuma? Paskaidro, kā tu katrā piemērā rēķināji.

Learn how to calculate the necessary amounts of tomatoes, meat, and cabbage in a stew where the ingredients are in a ratio of 1:2:7. This problem involves using basic algebra and proportions to solve for different scenarios, including 200 g of meat, 600 g of tomatoes, and 3 kg of total stew mass.

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