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Здравствуйте! У меня возникли сложности с таким вопросом: В одном растворе соли было на 20 % больше, чем во втором растворе. Смешав оба раствора, получили третий раствор, содержащий 24 % соли. Найдите массы исходных растворов, если известно, что в первом растворе было 2 кг соли, а во втором – 4 кг.
Условие Вашей задачи явно ошибочно изза его противоречивых пунктов! Если "в первом растворе было 2 кг соли, а во втором – 4 кг", то никак не может быть "В одном растворе соли было на 20 % больше, чем во втором растворе".
Если Вам очень нужно решить эту НЕправильную задачу, можно попытаться угадать пункт условия, где произошла ошибка и исправить эту ошибку. Например заменим фразу "В одном растворе соли было на 20 % больше, чем во втором растворе" на "В первом растворе [u]концентрация[/u] раствора соли была на 20 % выше, чем во втором растворе".
Тогда мы имеем: В первом растворе массой M1 было растворено к-во соли S1 = 2 кг . Концентрация K1 = S1 / M1 . Во втором растворе массой M2 было растворено к-во соли S2 = 4 кг . Концентрация K2 = S2 / M2 . Разность концентраций (K1 - K2) / K2 = 0,2 (0,2 - это 20%) Концентрацию смеси "24 % соли" запишем математически: (S1 + S2) / (M1 + M2) = 0,24
Теперь можно составить систему из 2х уравнений с 2мя неизвестными и решить её. Решать эту систему уравнений Вы можете любым удобным Вам способом (в тч используя OnLine-калькуляторы). Я люблю вычислять в популярном приложении Маткад (ссылка) . Маткад избавляет меня от ошибок. Маткад-скриншот прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Ответ : массы исходных растворов : 7,4 кг и 17,6 кг . Проверка сделана.
К сожалению, Вы ответили на мой вопрос об источнике этой задачи. Поэтому я склонен считать, что задача взята не из авторитетного источника, и её формулировка плохая. Это относится к предложению: Цитата: Mari
В одном растворе соли было на 20 % больше, чем во втором растворе.
По-моему, правильно так: "Массовая концентрация соли в первом растворе на 20 процентных пунктов больше, чем во втором растворе". Тогда, если ввести следующие обозначения: кг -- масса соли в первом растворе; -- масса первого раствора; -- масса соли во втором растворе; кг -- масса второго раствора, то из условия задачи получим такую систему уравнений:
Из второго уравнения системы получим, что (кг), Подставим это значение в первое уравнение системы. Тогда
Следовательно, кг -- масса первого раствора, (кг) -- масса второго раствора.
Об авторе:
Facta loquuntur.
Форма ответа
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Ответ : массы исходных растворов : 7,4 кг и 17,6 кг . Проверка сделана.
Mari 
кг -- масса соли в первом растворе;
-- масса первого раствора;
-- масса соли во втором растворе;
кг -- масса второго раствора,
(кг), 
Подставим это значение в первое уравнение системы. Тогда
кг -- масса первого раствора, 
(кг) -- масса второго раствора.