Question

Хозяйство собрало 38 946 кг слив,черешен и вишен.Половину этого количества составляли сливы.Черешен было в 3 раза меньше,чем слив,остальное - вишни.Сколько килограммов вишен собрало хозяйство.

Answer 1

38946÷2=19473сливы
19473÷3=6491черешня
38946-6491-19473=12982вишня

Answer 2

Problem Analysis

To solve this problem, we need to determine the weight of cherries and the weight of cherries. We are given that the total weight of plums, cherries, and cherries is 38,946 kg. Half of this weight is made up of plums, and the weight of cherries is three times less than the weight of plums. The remaining weight is cherries. We need to find the weight of cherries.

Solution

Let's denote the weight of plums as P, the weight of cherries as C, and the weight of cherries as V.

We are given the following information:

1. The total weight of plums, cherries, and cherries is 38,946 kg: - P + C + V = 38,946 kg

2. Half of this weight is made up of plums: - P = (1/2) * (P + C + V)

3. The weight of cherries is three times less than the weight of plums: - C = (1/3) * P

We can solve this system of equations to find the values of P, C, and V.

Solving the System of Equations

Let's substitute equation 2 into equation 1 to eliminate P:

(1/2) * (P + C + V) + C + V = 38,946 kg

Simplifying the equation:

P + 2C + 2V = 77,892 kg

Now, let's substitute equation 3 into the simplified equation:

(1/3) * P + 2C + 2V = 77,892 kg

Multiplying both sides of the equation by 3 to eliminate the fraction:

P + 6C + 6V = 233,676 kg

Now, we have a new equation:

P + 6C + 6V = 233,676 kg (Equation 4)

We can solve equations 4 and 1 simultaneously to find the values of P, C, and V.

Let's subtract equation 1 from equation 4:

(P + 6C + 6V) - (P + C + V) = 233,676 kg - 38,946 kg

Simplifying the equation:

5C + 5V = 194,730 kg

Dividing both sides of the equation by 5:

C + V = 38,946 kg

Now, we have a new equation:

C + V = 38,946 kg (Equation 5)

We can solve equations 5 and 3 simultaneously to find the values of C and V.

Let's substitute equation 3 into equation 5 to eliminate C:

(1/3) * P + V = 38,946 kg

Multiplying both sides of the equation by 3 to eliminate the fraction:

P + 3V = 116,838 kg

Now, we have a new equation:

P + 3V = 116,838 kg (Equation 6)

We can solve equations 6 and 5 simultaneously to find the values of P, C, and V.

Let's subtract equation 5 from equation 6:

(P + 3V) - (C + V) = 116,838 kg - 38,946 kg

Simplifying the equation:

P + 2V - C = 77,892 kg

Now, we have a new equation:

P + 2V - C = 77,892 kg (Equation 7)

We can solve equations 7 and 5 simultaneously to find the values of P, C, and V.

Let's add equation 5 to equation 7:

P + 2V - C + C + V = 77,892 kg + 38,946 kg

Simplifying the equation:

P + 3V = 116,838 kg

This is the same equation as equation 6. Therefore, equations 6 and 5 are equivalent.

Conclusion

From the analysis and solution, we can conclude that the weight of cherries collected by the farm is 38,946 kg.