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In a country, as much as wheat products....

In a country, as much as wheat products. `4%` wheat of it is eaten by mouses. Then `280` million ton wheat is imported. If `7%` wheat is eaten by mouses. Then 210 million ton wheat is imported more. What is the national production of wheat in the country if it is assumed that production is equal to requirement of one country.

A

`7000`

B

`8000`

C

`6900`

D

`7200`

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AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the national production of wheat in the country based on the information given about wheat consumption by mice and the amount of wheat imported. ### Step-by-Step Solution: 1. **Understanding the Problem**: - Let the total national production of wheat be \( P \). - According to the problem, when 4% of the wheat is eaten by mice, the country imports 280 million tons of wheat. - When 7% of the wheat is eaten by mice, the country imports an additional 210 million tons of wheat. 2. **Setting Up the Equations**: - If 4% of the wheat is eaten by mice, then the remaining wheat available for consumption is \( P - 0.04P = 0.96P \). - The amount of wheat that needs to be imported when 4% is eaten by mice is given as 280 million tons. Therefore: \[ 0.96P + 280 = P \] - Rearranging this gives: \[ P - 0.96P = 280 \implies 0.04P = 280 \implies P = \frac{280}{0.04} = 7000 \text{ million tons} \] 3. **Checking the Second Condition**: - Now, if 7% of the wheat is eaten by mice, the remaining wheat available for consumption is \( P - 0.07P = 0.93P \). - The amount of wheat that needs to be imported when 7% is eaten by mice is: \[ 0.93P + 280 + 210 = P \] - Rearranging gives: \[ P - 0.93P = 280 + 210 \implies 0.07P = 490 \implies P = \frac{490}{0.07} = 7000 \text{ million tons} \] 4. **Conclusion**: - Both conditions lead to the same national production of wheat. - Therefore, the national production of wheat in the country is **7000 million tons**. ### Final Answer: The national production of wheat in the country is **7000 million tons**.
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