Question

5 мешков картофеля и 3 мешка зерна вместе весят 420 кг, а 9 мешков картофеля и 3 мешка зерна в 594 кг.сколько весит весит мешок картофеля и зерна отдельно?

Answer 1

5 м карт + 3 м зерна =420 кг
9 м карт + 3 м зерна =594 кг
1 м карт -?
1 м зерна - ?

1) 594-420=174 (кг) - весят 4 м картофеля.
2) 174:4=43,5 (кг) - весит 1 мешок картофеля.
3) 420-(5•43,5)=202,5 (кг) - весят 3 мешка зерна.
4) 202,5:3=67,5 (кг) - весит 1 мешок зерна.

проверяем:
5•43,5+3•67,5=217,5+202,5=420
9•43,5+3•67,5=391,5+202,5=594

Ответ: 1 мешок картофеля весит 43,5 кг;
1 мешок зерна весит 67,5 кг.

Answer 2

Calculation of the Weight of a Bag of Potatoes and Grain Separately

To determine the weight of a bag of potatoes and grain separately, we can set up a system of equations based on the given information.

Let's assume the weight of a bag of potatoes is represented by P and the weight of a bag of grain is represented by G.

According to the information provided: - 5 bags of potatoes and 3 bags of grain together weigh 420 kg. - 9 bags of potatoes and 3 bags of grain together weigh 594 kg.

We can set up the following equations:

Equation 1: 5P + 3G = 420 (from the first statement) Equation 2: 9P + 3G = 594 (from the second statement)

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of elimination to solve the system:

Multiplying Equation 1 by 3 and Equation 2 by 5, we get:

Equation 3: 15P + 9G = 1260 Equation 4: 45P + 15G = 2970

Subtracting Equation 3 from Equation 4, we eliminate the variable G:

Equation 5: 30P = 1710

Dividing both sides of Equation 5 by 30, we find:

P = 57

Now, we can substitute the value of P back into Equation 1 to find the weight of a bag of grain:

5P + 3G = 420

Substituting P = 57, we have:

5(57) + 3G = 420

Simplifying, we get:

285 + 3G = 420

Subtracting 285 from both sides, we have:

3G = 135

Dividing both sides by 3, we find:

G = 45

Therefore, a bag of potatoes weighs 57 kg, and a bag of grain weighs 45 kg.