Question

На базе два предпринимателя закупили вместе 300 кг товара по цене 25 грн. за 1 кг. Первый предприниматель перевозит товар на расстояние 20 км. от базы а второй - на 30 км. Перевозки 100 кг товара на расстояние 1 км стоит 5 грн. Определите, сколько товара закупил первый предприниматель, если известно, что он потратил на закупку и перевозкой товара 1125 грн меньше, чем второй. помогите решить! Умоляю!!

Answer 1

Problem Analysis

We are given the following information: - Two entrepreneurs purchased a total of 300 kg of goods at a price of 25 UAH per 1 kg. - The first entrepreneur transported the goods a distance of 20 km from the base, while the second entrepreneur transported them a distance of 30 km. - The cost of transporting 100 kg of goods for a distance of 1 km is 5 UAH. - The first entrepreneur spent 1125 UAH less on purchasing and transporting the goods than the second entrepreneur.

We need to determine how much goods the first entrepreneur purchased.

Solution

Let's assume that the first entrepreneur purchased x kg of goods. Then the second entrepreneur purchased (300 - x) kg of goods.

The cost of purchasing the goods for the first entrepreneur is x * 25 UAH.

The cost of transporting the goods for the first entrepreneur is (x / 100) * 20 * 5 UAH.

The total cost for the first entrepreneur is x * 25 UAH + (x / 100) * 20 * 5 UAH.

The cost of purchasing the goods for the second entrepreneur is (300 - x) * 25 UAH.

The cost of transporting the goods for the second entrepreneur is ((300 - x) / 100) * 30 * 5 UAH.

The total cost for the second entrepreneur is (300 - x) * 25 UAH + ((300 - x) / 100) * 30 * 5 UAH.

According to the given information, the first entrepreneur spent 1125 UAH less than the second entrepreneur. So we can set up the following equation:

(x * 25 UAH + (x / 100) * 20 * 5 UAH) + 1125 UAH = (300 - x) * 25 UAH + ((300 - x) / 100) * 30 * 5 UAH

Now we can solve this equation to find the value of x, which represents the amount of goods purchased by the first entrepreneur.

Calculation

Let's solve the equation:

(x * 25 + (x / 100) * 20 * 5) + 1125 = (300 - x) * 25 + ((300 - x) / 100) * 30 * 5

Simplifying the equation:

25x + (x / 100) * 20 * 5 + 1125 = 7500 - 25x + ((300 - x) / 100) * 30 * 5

Multiplying through by 100 to remove the decimal:

2500x + x * 20 * 5 + 112500 = 750000 - 2500x + (300 - x) * 30 * 5

Expanding and simplifying:

2500x + 100x + 112500 = 750000 - 2500x + 15000 - 30x

Combining like terms:

2600x + 112500 = 765000 - 30x

Adding 30x to both sides:

2630x + 112500 = 765000

Subtracting 112500 from both sides:

2630x = 652500

Dividing both sides by 2630:

x = 248.28

Therefore, the first entrepreneur purchased approximately 248.28 kg of goods.

Answer

The first entrepreneur purchased approximately 248.28 kg of goods.