## EXPLORATION 1 Mixing Solutions
Aileen's Drugstore needs to prepare a 60-L mixture that is 40\% acid, using three concentrations of acid. The first concentration is 15% acid, the second is 35\% acid, and the third is 55\% acid. Because of the amounts of acid solution on hand, they need to use twice as much of the 35% solution as the 55% solution. How much of each solution should they use?
Let x= the number of liters of 15% solution used, y= the number of liters of 35% solution used, and z= the number of liters of 55% solution used.
(1) Explain how the equation x+y+z=60 is related to the problem.
(2) Explain how the equation 0.15x+0.35y+0.55z=24 is related to the problem.
(3) Explain how the equation y=2z is related to the problem.
(4) Write the system of three equations obtained from parts 1−3 in the form AX=B, where A is the coefficient matrix of the system. What are A,B, and X ?
(5) Solve the matrix equation in part 4.
(6) Interpret the solution in part 5 in terms of the problem situation.