На два платья и пять сарафанов ушло 18 м ткани, а на три таких же платья и десять таких же сарафанов ушло 32,5 м ткани. Сколько ткани требуется на одно платье и сколько на один сарафан

Обозначим платья за х, а сарафаны за у. И решим задачу, составив систему уравнений:

2х + 5у = 18

3х + 10у = 32,5

х = (18 — 5у)/2

Подставим х во второе уравнение:

3*(18 — 5у)/2 + 10у = 32,5

Сокращает 3 в числителе и 2 в знаменателе, получаем:

1,5 * (18 — 5у) + 10у = 32,5

27 — 7,5у + 10у = 32,5

-7,5 у + 10у = 32,5 — 27

2,5у = 5,5

у = 2,2

Тогда х = (18 — 5*2,2)/2

х = (18 — 11)/2

х = 7/2

х = 3,5

Ответ: на одно платье требуется 3,5 метров ткани, на один сарафан — 2,2 метра.

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