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5. Bottle A, containing 12L of 15% acid, is combined with bottle B, containing 3L of...

5. Bottle A, containing 12L of 15% acid, is combined with bottle B, containing 3L of 20% acid. Bottle C is 26% acid. How much of each solution is needed to have a 24L of 20% acid solution? What pH is the solution?

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5. When bottle A, containing 12L of 15% acid, is combined with bottle B, containing 3L of 20% acid, we get 15 L of acid with strength (12*15+3*20)/(12+3) = 240/15 = 16 % acid. Let x L of 16 % acid be combined with y L of 26 % acid to get 24 L of 20 % acid solution. Then x+y = 24 …(1) and x* 0.16 +y*0.26 = 24 * 0.20 or, 0.16x + 0.26y = 4.80 or,( on multiplying both the sides by 50) 8x + 13y = 240…(2). On solving these equations, we get x = 72/5 =14.4 and y = 48/5 = 9.6. Hence 14.4 L of 16 % acid should be combined with 9.6 L of 26 % acid to get 24 L of 20 % acid solution.

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