For the purpose of an experiment an acid solution between 4% and 6% is required 640 liters of 8% - Maths - Linear Inequalities

Question

For the purpose of an experiment an acid solution between
4% and 6% is required 640 liters of 8% acidsolution and a 2% acid
solution is available in the laboratory How many liters of the 2%
solution need to be added to the 8% solution?

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Let x litres of 2 % acid solution be added to 640 litres of 8 % solution . \Rightarrow % Strength = \frac{\frac{8}{100} \times 640 + \frac{2}{100} \times x}{640 + x} = \frac{1}{100} (\frac{5120 + 2 x}{640 + x}) According to question, strength should vary from 4 % to 6 % \Rightarrow \frac{4}{100} < \frac{1}{100} (\frac{5120 + 2 x}{640 + x}) < \frac{6}{100} Multiplying by 100, we get, 4 < (\frac{5120 + 2 x}{640 + x}) < 6 \Rightarrow \frac{5120 + 2 x}{640 + x} > 4 and \frac{5120 + 2 x}{640 + x} < 6 \Rightarrow 5120 + 2 x > 2560 + 4 x and 5120 + 2 x < 3840 + 6 x \Rightarrow 4 x - 2 x < 5120 - 2560 and 6 x - 2 x > 5120 - 3840 \Rightarrow 2 x < 2560 and 4 x > 1280 \Rightarrow x < 1280 and x > 320 \Rightarrow x \in (320, 1280) Hence quality of 2 % solution to be added must vary from 320 litres to 1280 litres . (Answer)

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For the purpose of an experiment an acid solution between 4% and 6% is required. 640 liters of 8% acidsolution and a 2% acid solution is available in the laboratory.How many liters of the 2% solution need to be added to the 8% solution?