Answer:
Step-by-step explanation:
Let x represent the quantity of 25% solution to be used. Then 65-x is the quantity of 12% solution needed. The amount of alcohol in the mix is ...
0.25x +0.12(65 -x) = 0.15(65)
0.13x +7.8 = 9.75 . . . . eliminate parentheses
0.13x = 1.95 . . . . . . subtract 7.8
x = 15 . . . . . . . . . . . divide by .13
65-x = 65-15 = 50
She needs 15 liters of 25% solution and 50 liters of 12% solution.
Answer:
12% = 50 liters
25% = 15 liters
Step-by-step explanation:
first we have to make two equations one that represents the amount of total liters and another that represents the amount of liter of alcohol
x = liters of 12% solution
y = liters of 25% solution
x + y = 65
12/100 * x + 25/100 * y = 15/100 * 65
we solve for x in the first equation
x + y = 65
x = 65 - y
we replace x in the second equation with (65 - y) and solve by solving for y
12/100 * x + 25/100 * y = 15/100 * 65
12/100 * (65 - y) + 25/100 * y = 15/100 * 65
7.8 - 0.12y + 0.25y = 9.75
- 0.12y + 0.25y = 9.75 - 7.8
0.13y = 1.95
y = 1.95/0.13
y = 15
we replace the value of y and solve
x = 65 - y
x = 65 - 15
x = 50
50 liters of the 12% solutions and 15 liters of the 25% solutions
