Question

Из 1 т молока получается 83 кг сыра или 45 кг масла. На сколько килограммов больше сыра, чем масла, получится из 20 т молока? Реши задачу разными способами

Answer 1

1 способ.
83 * 20 = 1660(кг) сыра из 20 т молока
45 * 20 = 900(кг) масла из 20 т молока
1660 - 900 = 760(кг) сыра больше, чем масла получится из 20 т молока
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2 способ.
83 - 45 = 38(кг) на 38 кг сыра больше чем масла получается из 1 т молока
38 * 20 = 760(кг) сыра больше, чем масла получится из 20 т молока

Answer 2

Task Analysis

To solve this problem, we need to determine the difference in kilograms between the amount of cheese and the amount of butter that can be produced from 20 tons of milk. We are given that 1 ton of milk produces 83 kg of cheese or 45 kg of butter.

Solution 1: Using Proportions

We can solve this problem using proportions. Let's set up a proportion to find the amount of cheese and butter that can be produced from 20 tons of milk.

Let x be the amount of cheese produced from 20 tons of milk. Let y be the amount of butter produced from 20 tons of milk.

We can set up the following proportion:

1 ton of milk produces 83 kg of cheese 20 tons of milk produces x kg of cheese

1 ton of milk produces 45 kg of butter 20 tons of milk produces y kg of butter

Using cross-multiplication, we can solve for x and y:

x = (20 tons of milk * 83 kg of cheese) / 1 ton of milk y = (20 tons of milk * 45 kg of butter) / 1 ton of milk

Now we can calculate the values of x and y:

x = (20 * 83) kg y = (20 * 45) kg

Finally, we can find the difference between the amount of cheese and the amount of butter:

difference = x - y

Let's calculate the values:

x = 20 * 83 = 1660 kg y = 20 * 45 = 900 kg difference = 1660 kg - 900 kg = 760 kg

Therefore, the difference between the amount of cheese and the amount of butter that can be produced from 20 tons of milk is 760 kg.

Solution 2: Using Subtraction

Alternatively, we can solve this problem by directly subtracting the amount of butter from the amount of cheese that can be produced from 20 tons of milk.

Let's calculate the values:

Amount of cheese = 20 tons of milk * 83 kg of cheese / 1 ton of milk = 20 * 83 = 1660 kg Amount of butter = 20 tons of milk * 45 kg of butter / 1 ton of milk = 20 * 45 = 900 kg

Difference = Amount of cheese - Amount of butter = 1660 kg - 900 kg = 760 kg

Therefore, the difference between the amount of cheese and the amount of butter that can be produced from 20 tons of milk is 760 kg.

Both solutions yield the same result.

Conclusion

The difference between the amount of cheese and the amount of butter that can be produced from 20 tons of milk is 760 kg.