a solution of 78% pesticide is to be mixed with a solution of 20% pesticide to form 174 liters of a 50% solution. How many liters of the 78% solution must be used?

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From the given information, you can write two equations...0.78x + 0.2y = 0.5(174)x + y = 174You can now solve the system by graphing, using either the substitution or elimination method, or by setting up a matrix equation.  I will use substitution...x + y = 174      y = 174 - x0.78x + 0.2(174 - x) = 0.5(174) 0.78x + 34.8 - 0.2x = 87                       0.58x = 52.2                              x = 90 liters of the 78% solutionIf you wanted to solve for y as well, you can substitute 90 for x into either of your original equations to get y = 84 liters of the 20% solution.