Предмет: Алгебра, автор: maftuna50

405 тонн груза перевозили 50 машин грузоподъёмностью 5 тонн
и 10 тонн. Сколько машин грузоподъёмностью 5 тонн и сколько
машин грузоподъёмностью 10 тонн принимали участие в перевозке?​

Ответы

Автор ответа: Zombynella
20

Ответ:

31 (машина) грузоподъёмностью 10 тонн

19 (машин) грузоподъёмностью 5 тонн

Объяснение:

х - машин грузоподъёмностью 5 тонн

у - машин грузоподъёмностью 10 тонн

По условию задачи машин всего было 50, груза всего 405 тонн, система уравнений:

х+у=50

5х+10у=405

Выразим х через у в первом уравнении и подставим выражение во второе уравнение (метод подстановки):

х=50-у

5(50-у)+10у=405

250-5у+10у=405

5у=405-250

5у=155

у=31 (машина) грузоподъёмностью 10 тонн

х=50-31=19 (машин) грузоподъёмностью 5 тонн

Проверка:

10*31=310 (тонн)

5*19=95 (тонн)

310+95=405 (тонн), всё верно.

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