Maths question
2014-12-26 10:21 pm
the liquid in bottle A contains 30% alcohol and 70% water (by volume).The liquid in bottle B contains 90% alcohol and10% water. If 1000 cm cube of the liquid in bottle A is takenout , at least how many cm cube of the liquid in bottle B should be used to mix with it so that the mixed liquid formed contains at least 50% alcohol ?
回答 (1)
2014-12-26 11:57 pm
✔ 最佳答案
Let x cm cube be the required amount of the liquid in bottle B should be used to mix.Note that in the mixture, the total volume is (1000 + x) cm cube.
The amount of alcohol (in cm cube) in the mixture is
1000(30%) + x(90%)
= 300 + 0.9x
Therefore,
(300 + 0.9x) / (1000 + x) ≥ 50%
300 + 0.9x ≥ 500 + 0.5x
0.4x ≥ 200
x ≥ 500
Therefore, at least 500 cm cube the liquid in bottle B should be used to mix with it so that the mixed liquid formed contains at least 50% alcohol.
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