How much of 30% alcoholsolution should be added to 75 liters of 21% alcohol solution to make it a 25%alcohol solution?
Answers
For this type of problem, it's often useful to make a table. Call the number of liters of the 30% solution x. Then, in the table, the first row will represent the 30% solution, the second row will represent the 90% solution, and the third row will represent the 70% solution:
TOTAL LITERS ALCOHOL CONCENTRATION LITERS OF ALCOHOL
x 0.3 0.3x
90 0.9 0.9(90)
x+90 0.7 0.7(x+90)
Since the first two solutions will be combined to create the third solution, write an equation to model that and solve for x:
0.3x + 0.9(90) = 0.7(x+90)
0.3x + 81 = 0.7x + 63
81 = 0.4x + 63
18 = 0.4x
45 = x
That means you need 45 liters of the 30% solution.