Question

Помогите, пожалуйста, решить задачу. При ремонте квартиры в первый день отрезали 1/3 линолеума и еще 4/5 метра. Во второй день 6/7 остатка и еще 1/5 метра. После чего в рулоне осталось 2/5 метра. Ск-ко метров линолеума было в рулоне первоначально?

Answer 1

Пусть в начале было х.
Тогда, отрезали $\frac{1}{3}$х + 

Answer 2

Давайте разберемся.

Пусть x - количество метров линолеума в рулоне первоначально.

Тогда по условию задачи у нас есть следующая система уравнений:

1) x - 1/3x - 4/5 = (2/3)x - 4/5 метра линолеума отрезали в первый день. 2) (2/3)x - 6/7 * (2/3)x - 1/5 = (6/7)x - 6/21x - 1/5 метра линолеума отрезали во второй день. 3) (6/7)x - 6/21x - 1/5 - 2/5 = (6/7)x - 6/21x - 3/5 метра линолеума осталось в рулоне.

Теперь решим эту систему уравнений:

1) (2/3)x - 4/5 = (2/3)x - 12/15 - 4/5 = (2/3)x - 12/15 - 12/15 = (2/3)x - 24/15 = (2/3)x - 8/5 метра линолеума отрезали в первый день.

2) (6/7)x - 6/21x - 1/5 = (6/7)x - 2/7x - 1/5 = (6/7)x - 2/7x - 14/35 = (6/7)x - 2/7x - 2/5 метра линолеума отрезали во второй день.

3) (6/7)x - 6/21x - 3/5 = (6/7)x - 2/7x - 3/5 = (6/7)x - 2/7x - 21/35 = (6/7)x - 2/7x - 3/5 метра линолеума осталось в рулоне.

Теперь подставим полученные значения в последнее уравнение:

(6/7)x - 2/7x - 3/5 = 2/3x - 8/5 - 2/7x - 3/5 = 2/3x - 8/5 - 6/15x - 9/15 = 2/3x - 8/5 - 6/15x - 9/15 = 2/3x - 6/15x - 8/5 - 9/15 = 2/3x - 6/15x - 24/15 - 9/15 = 2/3x - 6/15x - 33/15 = 2/3x - 2/10x - 22/10 = 2/3x - 2/10x - 22/10 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 3/15x - 11 = 2/3x - 3/15x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 = 2/3x - 1/5x - 11 =