Question

В двух мешках было 75 кг крупы. После того как из первого мешка продали 12 кг, а из второго 18 кг, в первом мешке крупы оказалось в 2 раза больше, чем во втором. Сколько килограммов крупы было в каждом мешке первоначально?

Answer 1

За х кг примем вес крупы в 1-м мешке; 
(75-х)кг - вес крупы во втором мешке: 
(х-12)кг осталось в 1-м мешке после продажи; 
(75-х-18)=(57-х)кг осталось во 2-м мешке после продажи. 
В условии скзано, что в 1-м мешке осталось в 2 раза больше, поэтому составим равенство следующее: х-12=(57-х)*2. Нужно решить это уравнение. Получится х=42(кг) - первоначальный вес 1-го мешка; 
во втором было первоначально (75-х)=75-42=33(кг).

Answer 2

Problem Analysis

We are given two bags of grain, and the total weight of the grain in both bags is 75 kg. After selling 12 kg from the first bag and 18 kg from the second bag, the weight of the grain in the first bag is twice the weight of the grain in the second bag. We need to determine the initial weight of the grain in each bag.

Solution

Let's assume the initial weight of the grain in the first bag is x kg, and the initial weight of the grain in the second bag is y kg.

According to the given information, we have the following equations:

Equation 1: x + y = 75 (the total weight of the grain in both bags is 75 kg)

Equation 2: x - 12 = 2(y - 18) (the weight of the grain in the first bag is twice the weight of the grain in the second bag after selling 12 kg from the first bag and 18 kg from the second bag)

We can solve this system of equations to find the values of x and y.

Solving the Equations

Let's solve the system of equations using the substitution method.

From Equation 1, we can express x in terms of y: x = 75 - y

Substituting this value of x into Equation 2, we get: 75 - y - 12 = 2(y - 18)

Simplifying the equation: 63 - y = 2y - 36

Bringing all the terms involving y to one side: 3y = 99

Dividing both sides by 3: y = 33

Substituting the value of y back into Equation 1, we can find x: x + 33 = 75 x = 75 - 33 x = 42

Answer

The initial weight of the grain in the first bag was 42 kg, and the initial weight of the grain in the second bag was 33 kg.

Verification

To verify our solution, let's check if the conditions given in the problem are satisfied:

1. After selling 12 kg from the first bag, the weight of the grain in the first bag is 42 - 12 = 30 kg. 2. After selling 18 kg from the second bag, the weight of the grain in the second bag is 33 - 18 = 15 kg. 3. The weight of the grain in the first bag is twice the weight of the grain in the second bag: 30 = 2 * 15.

Therefore, our solution is correct.