A scientist needs 65 liters of a 15% alcohol solution. She has available 25% and a 12% solution. How many liters of the 25% and how many liters of the 12% solutions should she mix to make the 15% solution?

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.

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

good luck on your studies! : )

david edward.

2160ft3

step-by-step explanation: