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We wish to obtain a 40% solution of nitric acid by mixing a 20% solution in a 70% solution of acid. What percentage of the final solution should be taken from the 20% and 70% solutions? Solution:
 Solution 1 Solution 2 Mixture Nitric Acid 20% 70% 40% Others 80% 30% 60% x y F

$$x+y=F$$

$$y = F-x$$

$$0.2x+ 0.7y = 0.4 F$$

$$0.2x+ 0.7(F-x) = 0.4 F$$

$$0.2x +0.7F-0.7x = 0.4F$$

$$0.5 x = 0.3F$$

$$x = 0.6F$$

$$y = 0.4F$$

60% should be taken from the 20% solution and 40% from the other solution.