Question

ДОМАШНЕЕ ЗАДАНИЕ 9Реши задачу разными способами.Космическое агентство решило заняться«Космическимсельским хозяйством». Учёные стали изучать влияние усло-вий космоса на растения. В специальной теплице посадили900 растений, причём 630 из них были овощными культура-Ми, а остальные злаки. Овощные рассадили по 35 штук накаждую полку, а злаки по 30 штук. Сколько полок потребо-валось?Как можно решить уравнением?

Answer 1

To solve this problem, we need to determine the number of shelves required for the 900 plants. We know that 630 of the plants are vegetables, and the remaining plants are grains. The vegetables are arranged with 35 plants per shelf, while the grains are arranged with 30 plants per shelf.

To find the number of shelves needed, we can divide the total number of plants by the number of plants per shelf for each type.

Let's calculate it step by step:

1. Calculate the number of shelves for vegetables: - Number of vegetable plants: 630 - Number of vegetable plants per shelf: 35 - Number of shelves for vegetables = Number of vegetable plants / Number of vegetable plants per shelf

Number of shelves for vegetables = 630 / 35 = 18 shelves

2. Calculate the number of shelves for grains: - Number of grain plants: 900 - 630 = 270 - Number of grain plants per shelf: 30 - Number of shelves for grains = Number of grain plants / Number of grain plants per shelf

Number of shelves for grains = 270 / 30 = 9 shelves

3. Calculate the total number of shelves required: - Total number of shelves = Number of shelves for vegetables + Number of shelves for grains

Total number of shelves = 18 + 9 = 27 shelves

Therefore, a total of 27 shelves are required for the 900 plants in the greenhouse.

We can also solve this problem using an equation. Let's denote the number of shelves for vegetables as 'x' and the number of shelves for grains as 'y'. We can set up the following equation:

35x + 30y = 900

To solve this equation, we can use various methods such as substitution, elimination, or graphing. Let's solve it using the substitution method:

1. Solve the equation for 'x' in terms of 'y': - 35x = 900 - 30y - x = (900 - 30y) / 35

2. Substitute the value of 'x' in the equation: - (900 - 30y) / 35 + y = 900 / 35 - (900 - 30y + 35y) / 35 = 900 / 35 - (5y + 900) / 35 = 900 / 35

3. Simplify the equation: - 5y + 900 = 900 - 5y = 0 - y = 0

4. Substitute the value of 'y' back into the equation for 'x': - x = (900 - 30 * 0) / 35 - x = 900 / 35 - x = 25.71

Since the number of shelves cannot be a decimal, we round up to the nearest whole number.

Therefore, the number of shelves for vegetables is 26, and the number of shelves for grains is 0. The total number of shelves required is 26 + 0 = 26 shelves.

Both methods yield the same result, which is 26 shelves required for the 900 plants in the greenhouse.