Question

Logan wants to mix a 19% acid solution with a 44% acid solution to get 14 L of a 38% acid solution. How many liters of the 19% solution and how many liters of the 44% solution should be mixed? If necessary, write your answer as a fraction or mixed number in simplest form.

Answer 1

Let x liters of 19 % acid solution be mixed with y liters of 44 % acid solution to get 14 liters of 38% acid solution. Then x+y = 14…(1)

Also, x*0.19 +y* 0.44 = 14* 0.38 or, on multiplying both the sides by 100, we get 19x +44y = 532…(2).

From the 1^st equation, we get y = 14-x.On substituting y = 14-x in the 2^nd equation, we get 19x +44(14-x) = 532 or, 19x +616-44x = 532 or, -25x = 532-616 = -84 so that x = 84/25 = 3.36 liters. Then y = 14-3.36 = 10.64.

Thus, 3.36 liters of 19 % acid solution should be mixed with 10.64 liters of 44 % acid solution to get 14 liters of 38% acid solution.