Решить интегрирование по частям, если не возможно непосредственное интегрирование или интегрирование с заменой (два номера + с объяснением для 1 курса)

х литров 55%-го раствора взяли для приготовления нового раствора;

0.55х - объем соли в 55%-ом растворе

(100-х) литров 30%-го раствора взяли для приготовления нового раствора

0.3(100-х) - объем соли в 30%-ом растворе

0,55х + 0.3(100-х) - объем соли в новом растворе

45% от 100 л = 0,45 * 100 = 45 объем соли в новом растворе

Уравнение.

0,55х + 0.3·(100-х) = 45

0,55х + 30 - 0.3х = 45

0,25х = 45 - 30

0,25х = 15

х = 15 : 0,25

х = 60 литров 55%-го раствора взяли

100 - 60 = 40 литров 30%-го раствора использовали для приготовления нового раствора.

ответ: 60л; 40л

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