how many liters of a 70 acid solution must be mixed with a 1

how many liters of a 70% acid solution must be mixed with a 15% acid solution to get 330L of a 60% acid solution?

Solution

Let x liters of 70 % acid solution be mixed with y liters of 15 % acid solution to get 330L of 60 % acid solution. Then, we have x + y = 330 ...(1) and 0.7x + 0.15y = 330*0.6 = 198 or, 70x + 15y = 19800 ...(2) On multiplying both the sides of the 1st equation by 15, we get 15x + 15y = 330 * 15 = 4950...(3). Now, on subtracting the 3rd equation from the 2nd equation, we get 70x + 15y - 15x - 15y = 19800 - 4950 or, 55x = 14850 so that x =14850/55 = 270 . Then, from the 1st equation, we have y = 330 - x = 330 - 270 = 60. Thus, 270 liters of 70 % acid solution has to be mixed with 60 liters of 15 % acid solution to get 330L of 60 % acid solution.