Question

В одном овощехранилище было 440 тонн картофеля, а в другом - 408 тонн .Из первого хранилища ежедневно вывозили по 60 тонн картофеля, а во второе ежедневно завозил по 48 тонн. Через сколько дней во втором овощехранилище окажется в три раза больше картофеля, чем в первом? Обозначив искомое число дней буквой x, выразите: а)количество тонн картофеля, вывезено за x дней из первого овощехранилища ; б)количество тонн картофеля, завезённое за за x дней во второе овощехранилище; в)количество тонн картофеля, оставшиеся через x дней в первом овощехранилище; г)количество тонн картофеля , оказавшее через x дней во втором овощехранилище. Сравните количества картофеля, оказавшиеся через x дней в овощехранилищах, и запишите уравнение.Решите уравнение и запишите ответ на вопрос задачи. Дополнительные вопросы 1. На сколько процентов больше было картофеля в первом овощехранилище, чем во втором? 2.На сколько процентов больше оказалось картофеля во втором овощехранилище , чем в первом через два дня?

Answer 1

А) 60*х
б) 48*х
в) 440-60*х
г) 408+48*х

3*(440-60х)=(408+48х)
1320-180х=408+48х
-180х-48х=408-1320
228х=912
х=4
Ответ: через 4 дня
1) 7,(27)% больше
2) 440-60*2=440-120=320 т. - в первом
    408+2*48=408+96=504 т - во втором
504:320*100-100=57,5% больше

Answer 2

Problem Analysis

We are given the following information: - The first storage contains 440 tons of potatoes. - The second storage contains 408 tons of potatoes. - From the first storage, 60 tons of potatoes are taken out daily. - To the second storage, 48 tons of potatoes are added daily.

We need to find the number of days it will take for the second storage to have three times more potatoes than the first storage.

To solve this problem, we can set up equations to represent the quantities of potatoes in each storage after x days.

Problem Solution

Let's solve the problem step by step.

Step 1: Let's find the quantity of potatoes taken out from the first storage after x days.

The quantity of potatoes taken out from the first storage after x days can be calculated by multiplying the daily quantity taken out (60 tons) by the number of days (x):

a) Quantity of potatoes taken out from the first storage after x days:

60 * x

Step 2: Let's find the quantity of potatoes added to the second storage after x days.

The quantity of potatoes added to the second storage after x days can be calculated by multiplying the daily quantity added (48 tons) by the number of days (x):

b) Quantity of potatoes added to the second storage after x days:

48 * x

Step 3: Let's find the quantity of potatoes remaining in the first storage after x days.

The quantity of potatoes remaining in the first storage after x days can be calculated by subtracting the quantity taken out from the initial quantity in the first storage:

c) Quantity of potatoes remaining in the first storage after x days:

440 - (60 * x)

Step 4: Let's find the quantity of potatoes in the second storage after x days.

The quantity of potatoes in the second storage after x days can be calculated by adding the initial quantity in the second storage to the quantity added:

d) Quantity of potatoes in the second storage after x days:

408 + (48 * x)

Step 5: Let's set up an equation to represent the condition that the quantity of potatoes in the second storage is three times more than the quantity in the first storage.

The equation can be written as:

3 * (440 - (60 * x)) = 408 + (48 * x)

Step 6: Let's solve the equation to find the value of x.

Simplifying the equation:

1320 - 180x = 408 + 48x

Rearranging the terms:

1320 - 408 = 48x + 180x

912 = 228x

Dividing both sides by 228:

x = 912 / 228

x = 4

Therefore, it will take 4 days for the second storage to have three times more potatoes than the first storage.

Additional Questions:

1. To find the percentage difference in the quantity of potatoes between the first and second storage, we can use the formula:

Percentage Difference = ((Second Quantity - First Quantity) / First Quantity) * 100

Substituting the values:

Percentage Difference = ((408 - 440) / 440) * 100

Percentage Difference = (-32 / 440) * 100

Percentage Difference = -7.27%

Therefore, the quantity of potatoes in the first storage is approximately 7.27% less than the quantity in the second storage.

2. To find the percentage difference in the quantity of potatoes in the second storage compared to the first storage after two days, we can use the formula:

Percentage Difference = ((Second Quantity - First Quantity) / First Quantity) * 100

Substituting the values:

Quantity of potatoes in the first storage after two days = 440 - (60 * 2) = 320 tons

Quantity of potatoes in the second storage after two days = 408 + (48 * 2) = 504 tons

Percentage Difference = ((504 - 320) / 320) * 100

Percentage Difference = (184 / 320) * 100

Percentage Difference = 57.5%

Therefore, the quantity of potatoes in the second storage is approximately 57.5% more than the quantity in the first storage after two days.

Summary

- The quantity of potatoes taken out from the first storage after x days is given by 60 * x. - The quantity of potatoes added to the second storage after x days is given by 48 * x. - The quantity of potatoes remaining in the first storage after x days is given by 440 - (60 * x). - The quantity of potatoes in the second storage after x days is given by 408 + (48 * x). - It will take 4 days for the second storage to have three times more potatoes than the first storage. - The quantity of potatoes in the first storage is approximately 7.27% less than the quantity in the second storage. - The quantity of potatoes in the second storage is approximately 57.5% more than the quantity in the first storage after two days.