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Консультация № 121938
06.02.2008, 14:18
0.00 руб.
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1
Здраствуйте, у меня такая задача:
Груз вначале погрузили в вагоны вместимостью по 80 тонн, но один
вагон остался загружен не полностью. Тогда весь груз переложили в
вагоны вместимостью по 60 тонн. При этом понадобилось на 8 вагонов
больше, и все равно один вагон остался загружен не полностью.
Наконец, груз переложили в вагоны вместимостью по 50 тонн. При
этом понадобилось еще на 5 вагонов больше, и все вагоны оказались
полностью загруженными. Сколько было тонн груза ?
Груз вначале погрузили в вагоны вместимостью по 80 тонн, но один
вагон остался загружен не полностью. Тогда весь груз переложили в
вагоны вместимостью по 60 тонн. При этом понадобилось на 8 вагонов
больше, и все равно один вагон остался загружен не полностью.
Наконец, груз переложили в вагоны вместимостью по 50 тонн. При
этом понадобилось еще на 5 вагонов больше, и все вагоны оказались
полностью загруженными. Сколько было тонн груза ?
Обсуждение
Неизвестный
06.02.2008, 16:33
общий
это ответ
Здравствуйте, Понамарёв Александр Викторович!
Если в конечном итоге понадобилось х вагонов по 50 т в каждом, то груза было 50х т.
Тогда в предыдущем случае было х-5 вагонов; при таком раскладе груза было 60(х-6)+y, где y<60
60(х-6)+y = 50x => 0< y = 360 - 10x < 60 => 30 < x < 36
В самом первом раскладе вагонов было х-13, 80(х-14)+z - весь груз.
80(х-14)+z = 50х => 0< z = 1120 - 30x < 80 => 34 + 2/3 < x < 37 + 1/3
пересекая эти два ответа, получаем 34 + 2/3 < x < 36 Т.к. х вагонов - число целое, однозначно получаем х = 35 => груза было 1750т.
Если в конечном итоге понадобилось х вагонов по 50 т в каждом, то груза было 50х т.
Тогда в предыдущем случае было х-5 вагонов; при таком раскладе груза было 60(х-6)+y, где y<60
60(х-6)+y = 50x => 0< y = 360 - 10x < 60 => 30 < x < 36
В самом первом раскладе вагонов было х-13, 80(х-14)+z - весь груз.
80(х-14)+z = 50х => 0< z = 1120 - 30x < 80 => 34 + 2/3 < x < 37 + 1/3
пересекая эти два ответа, получаем 34 + 2/3 < x < 36 Т.к. х вагонов - число целое, однозначно получаем х = 35 => груза было 1750т.
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