Question

Один фермер привёз на рынок 5 тонн ячменя, который он хотел бы продать по 990 зедов за тонну, и 6 тонн ржи по 970 зедов за тонну (зед — условная денежная единица). У другого фермера 6 тонн ячменя по 980 зедов за тонну и 7 тонн ржи тоже по 980 зедов за тонну. Каждый фермер согласен отдать весь свой товар, если итоговая сумма совпадёт с той, которую он намеревался выручить за всю партию. Перекупщик хочет скупить обе партии товара, назначив одни и те же для обоих фермеров цены ячменя и ржи. Какие именно цены он должен назначить, чтобы скупить обе партии товара?

Answer 1

Первый фермер хочет получить 5*990+6*970=10770 зедов, а второй
6*980+7*980=12740 зедов
пусть перекупщику надо назаначить цену за тонну ячменя х зедов, а за тонну ржи у зедов
тогда
5x+6y=10770
6x+7y=12740
решаем эту систему
y=(10770-5x)/6
6x+7(10770-5x)/6=12740
36x+7(10770-5x)=76440
36x+75390-35x=76440
x=1050
y=(10770-5*1050)/6=920

Answer 2

Problem Analysis

We have two farmers who want to sell their crops: Farmer A has 5 tons of barley and 6 tons of rye, while Farmer B has 6 tons of barley and 7 tons of rye. Each farmer has a specific price in mind for their crops. The question is, what prices should the buyer offer for both barley and rye in order to purchase all the crops?

Solution

To find the prices that the buyer should offer, we need to calculate the total amount of money each farmer wants to receive for their crops and set it equal to the total amount the buyer is willing to pay.

Let's assume the buyer offers x zeds per ton of barley and y zeds per ton of rye.

For Farmer A: - The total amount of money Farmer A wants to receive for the barley is 5 tons * 990 zeds/ton = 4950 zeds. - The total amount of money Farmer A wants to receive for the rye is 6 tons * 970 zeds/ton = 5820 zeds.

For Farmer B: - The total amount of money Farmer B wants to receive for the barley is 6 tons * 980 zeds/ton = 5880 zeds. - The total amount of money Farmer B wants to receive for the rye is 7 tons * 980 zeds/ton = 6860 zeds.

The total amount the buyer is willing to pay is the sum of the amounts Farmer A and Farmer B want to receive: - Total amount the buyer is willing to pay for the barley: 4950 zeds + 5880 zeds = 10830 zeds. - Total amount the buyer is willing to pay for the rye: 5820 zeds + 6860 zeds = 12680 zeds.

To find the prices for barley and rye that the buyer should offer, we need to divide the total amount the buyer is willing to pay by the total weight of each crop.

For barley: - Price per ton of barley = Total amount the buyer is willing to pay for barley / Total weight of barley = 10830 zeds / (5 tons + 6 tons) = 990 zeds/ton.

For rye: - Price per ton of rye = Total amount the buyer is willing to pay for rye / Total weight of rye = 12680 zeds / (6 tons + 7 tons) = 980 zeds/ton.

Therefore, the buyer should offer 990 zeds/ton for barley and 980 zeds/ton for rye in order to purchase all the crops.

Answer

The buyer should offer 990 zeds/ton for barley and 980 zeds/ton for rye in order to purchase all the crops.