Маша и Медведь вместе съели \(140\) булочек и банку варенья, начав и закончив одновременно. Сначала Маша ела варенье, а Медведь — булочки, но в какой-то момент они поменялись. Медведь и то, и другое ест в три раза быстрее Маши. Сколько булочек съел Медведь, если варенья они съели поровну?
Решение
Медведь съел свою половину банки варенья в \(3\) раза быстрее, чем Маша, значит, у него еще осталось в \(3\) раза больше времени на кушанье булочек.
Т.к. Медведь ест булочки в \(3\) раза быстрее, чем Маша и еще у него осталось в \(3\) раза больше времени (он съел в \(3\) раза быстрее свою половину банки варенья), то он съедает в \(3⋅3=9\) раз больше булочек, чем Маша (\(9\) булочек съедает Медведь, в то время как Маша только \(1\) булочку).
Получается, что в отношении \(9:1\) едят Медведь и Маша булочки. Всего получается \(10\) долей, значит, \(1\) доля равна \(140:10=14\). В итоге, Медведь съел \(14⋅9=126\) булочек.
Ответ: \(126\).
Источник: ЕГЭ 2022. Единый государственный экзамен. Математика. Базовый уровень. Готовимся к итоговой аттестации. Учебное пособие (вариант №28) (Купить книгу)
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