Предмет: Математика, автор: Iproblem4034

У купца есть 6 мешков, которые весят 14, 16, 17, 18, 21 и 27 кг. Один мешок заполнен репой, а каждый из оставшихся либо луком, либо морковью. Купец знает, что суммарный вес моркови в два раза больше суммарного веса лука. В каком мешке может находиться репа? Укажите все возможные варианты: Мешок весом 14 кг Мешок весом 16 кг Мешок весом 17 кг Мешок весом 18 кг Мешок весом 21 кг < Мешок весом 27 кг​

Ответы

Автор ответа: volna7
0

Відповідь:

1 вариант:

Репа -> 14 кг.

Лук -> 16 + 17 = 33 кг.

Морковь -> 18 + 21 + 27 = 66 кг.

2 вариант:

Репа -> 17 кг.

Лук -> 14 + 18 = 32 кг.

Морковь -> 16 + 21 + 27 = 64 кг.

Покрокове пояснення:

Суммарный вес всех мешков:

14 + 16 + 17 + 18 + 21 + 27 = 113 кг.

По условию задачи суммарный вес всех мешков с морковью в два раза больше суммарного веса всех мешков с луком, значит суммарный вес всех мешков с морковью и луком вместе должен быть кратен числу 3. То есть, когда мы заберем один мешок с репой суммарный вес всех оставшихся мешков должен быть кратен числу 3. Таких варианта два:

1 вариант:

Репа -> 14 кг.

Лук -> 16 + 17 = 33 кг.

Морковь -> 18 + 21 + 27 = 66 кг.

2 вариант:

Репа -> 17 кг.

Лук -> 14 + 18 = 32 кг.

Морковь -> 16 + 21 + 27 = 64 кг.

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