Question

У двох мішках було 57 кг цукру. Із першого мішка відсипали 1/3 цукру, а з другого — 70 % цукру. Після цього в першому мішку цукру стало у 2 рази більше, ніж у другому. Скільки цукру було у кожному мішку спочатку?

Answer 1

в 1 мешке - х

во 2 мешке - у

составляем 2 уравнения

1)х+у=57

 

2)(х-1/3х):(у-0,7у)=2

2/3х^0,3y=2

2/3x:3/10y=2

20x:9y=2

из 1 уравнения выражаем х

х=57-у

подставляем во второе

20(57-y)/9у=2

1140-20у=18у

38у=1140

у=30 (кг) - в 1 мешке

57-30=27 (г) - во 2 мешке

 

 

 

 

Answer 2

В першому мішку було спочатку 38 кг, а в другому 19кг

Answer 3

Problem Analysis

We are given two bags of sugar with a total weight of 57 kg. From the first bag, 1/3 of the sugar is removed, and from the second bag, 70% of the sugar is removed. After this, the amount of sugar in the first bag becomes twice the amount in the second bag. We need to find the initial amount of sugar in each bag.

Solution

Let's assume the initial amount of sugar in the first bag is x kg and in the second bag is y kg.

According to the given information: 1. From the first bag, 1/3 of the sugar is removed. So, the remaining sugar in the first bag is (2/3)x kg. 2. From the second bag, 70% of the sugar is removed. So, the remaining sugar in the second bag is (30/100)y kg, which can be simplified to (3/10)y kg. 3. The remaining sugar in the first bag is twice the amount in the second bag. So, we can write the equation: (2/3)x = 2 * (3/10)y.

To solve this equation, we can simplify it by multiplying both sides by 30 to eliminate the fractions: 20x = 18y.

Now, we have two equations: 1. x + y = 57 (since the total weight of the two bags is 57 kg). 2. 20x = 18y.

We can solve these equations simultaneously to find the values of x and y.

Let's solve the equations:

From equation 2, we can express x in terms of y: x = (18y) / 20, which simplifies to x = (9y) / 10.

Substituting this value of x in equation 1, we get: (9y) / 10 + y = 57.

Multiplying both sides by 10 to eliminate the fraction, we have: 9y + 10y = 570.

Combining like terms, we get: 19y = 570.

Dividing both sides by 19, we find: y = 30.

Substituting this value of y back into equation 1, we can find x: x + 30 = 57, x = 57 - 30, x = 27.

Therefore, the initial amount of sugar in the first bag was 27 kg, and in the second bag was 30 kg.

Answer: The initial amount of sugar in the first bag was 27 kg, and in the second bag was 30 kg.