How many liters each of a 15% acid solution and a 60% acid solution must be used to produce 90 liters of a 45% acid solution? (Round to tw decimal places if necessary.)
Let x be the number of liters of the 15% acid solution and y be the number of liters of the 60% acid solution. We have the following two equations:
x + y = 90 (equation 1)
0.15x + 0.60y = 0.45(90) (equation 2)
Let's solve the system of equations.
From equation 1, we have:
x = 90 - y
Substituting this into equation 2, we get:
0.15(90 - y) + 0.60y = 40.5
13.5 - 0.15y + 0.60y = 40.5
0.45y = 27
y = 60
Substituting this value back into equation 1, we get:
x + 60 = 90
x = 30
Therefore, we need to use 30 liters of the 15% acid solution and 60 liters of the 60% acid solution to produce 90 liters of a 45% acid solution.