Question

Площадь земли, засеяной пшеницей, в 5 раз больше площади, засеянной рожью, а площадь, засеянной овсом, в 3 раза мееньше площади, засеянной пшеницы. Сколька га земли засеяно каждой культурой, если овсом засеяно на 80 га больше, чем рожью?

Answer 1

Х га - засеяно рожью
5х га - засеяно пшеницей
5х/3 га - засеяно овсом

5х/3 - х = 80
5х - 3х = 240
2х = 240
х = 120 га - засеяно рожью
120 * 5 = 600 га - засеяно пшеницей
120 * 5 : 3 = 200 га  - засеяно овсом

Answer 2

Calculation of Land Area for Each Crop

To calculate the land area for each crop, we need to determine the area of land sown with wheat, rye, and oats. We are given that the area sown with wheat is 5 times larger than the area sown with rye, and the area sown with oats is 3 times smaller than the area sown with wheat. Additionally, we know that the area sown with oats is 80 hectares larger than the area sown with rye.

Let's assign variables to represent the areas of land sown with each crop: - Let W be the area sown with wheat. - Let R be the area sown with rye. - Let O be the area sown with oats.

Based on the given information, we can set up the following equations:

1. The area sown with wheat is 5 times larger than the area sown with rye: W = 5R.

2. The area sown with oats is 3 times smaller than the area sown with wheat: O = (1/3)W.

3. The area sown with oats is 80 hectares larger than the area sown with rye: O = R + 80.

To find the values of W, R, and O, we can solve this system of equations.

Solving the System of Equations

Substituting equation 1 into equation 2, we get: (1/3)W = (1/3)(5R) = (5/3)R.

Substituting equation 3 into equation 2, we get: (5/3)R = R + 80.

Now, let's solve this equation for R:

(5/3)R = R + 80

Multiplying both sides by 3 to eliminate the fraction: 5R = 3R + 240

Subtracting 3R from both sides: 2R = 240

Dividing both sides by 2: R = 120

Now that we have the value of R, we can substitute it back into equation 1 to find W: W = 5R = 5(120) = 600.

Finally, we can substitute the value of R into equation 3 to find O: O = R + 80 = 120 + 80 = 200.

Therefore, the area of land sown with each crop is as follows: - Wheat: 600 hectares - Rye: 120 hectares - Oats: 200 hectares.

Please note that these calculations are based on the given information and the assumptions made.