Question

ФЕрмер продал картофель 3 покупателям: первому 1/6 всего картофеля, второму 2/5 остатка, а третьему 1/2 нового остатка и последние 400 кг. Сколько кг картофеля было к фермера?

Answer 1

Все - х
1 ---- 1/6 х
2-------2/5*(х-1/6х)=2/5*5/6х=1/3х
3------1/2*(х-(1/6х+1/3х))=1/2*(х-1/2 х)=1/2*1/2х=1/4х
1/6х+1/3х+1/4х+400=х
3/4х+400=х
х-3/4х=400
1/4х=400
х=1600

Answer 2

Problem Analysis

A farmer sold potatoes to three buyers. The first buyer purchased 1/6 of the total potatoes, the second buyer purchased 2/5 of the remaining potatoes, and the third buyer purchased 1/2 of the new remaining potatoes, leaving 400 kg of potatoes. We need to determine the total weight of potatoes the farmer had initially.

Solution

Let's assume the total weight of potatoes the farmer had initially is x kg.

The first buyer purchased 1/6 of the total potatoes, which is (1/6) * x kg.

The remaining potatoes after the first buyer's purchase is (5/6) * x kg.

The second buyer purchased 2/5 of the remaining potatoes, which is (2/5) * (5/6) * x kg.

The new remaining potatoes after the second buyer's purchase is (3/5) * (5/6) * x kg.

The third buyer purchased 1/2 of the new remaining potatoes, which is (1/2) * (3/5) * (5/6) * x kg.

The weight of potatoes left after the third buyer's purchase is 400 kg.

Therefore, we can set up the equation:

(1/2) * (3/5) * (5/6) * x = 400

Simplifying the equation:

(1/2) * (3/5) * (5/6) * x = 400

(3/10) * (5/6) * x = 400

(1/4) * x = 400

x = 400 * 4

x = 1600 kg

Therefore, the farmer initially had 1600 kg of potatoes.

Answer

The farmer initially had 1600 kg of potatoes.