Предмет: Математика, автор: думающий

10 слив имеют такую же массу, как 3 яблока и 1 груша, а 2 сливы и 1 яблоко - как 1 груша. Сколько нужно взять слив, чтобы их масса была равна массе 1 груши?

Ответы

Автор ответа: Влад1995308

Обозначаем массу сливы за x, массу яблок - за y, а груш - за z.
Тогда мы имеем систему из двух уравнений:
3y+z=10x
2x+y=z

10x-3y=z
2x+y=z
Отсюда следует, что 2x+y=10x-3y
Переносим всё влево и приводим подобные:
-8x=-4y
2x=y
Берём уравнение 3y+z=10x и подставляем вместо y 2x:
3*2x+z=10x
6x+z=10x
z=10x-6x
z=4x
Выходит, масса одной груши равна массе четырёх слив. То есть, ответ: 4.

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