Question

Darryl wants to make 22 L of a 26% alcohol solution by mixing together a 36% alcohol solution and a 14% alcohol solution. How much of each solution must he use?

A) 14 L of 36% solution and 8 L of 14% solution
B) 18 L of 36% solution and 4 L of 14% solution
C) 12 L of 36% solution and 10 L of 14% solution
D) 8 L of 36% solution and 14 L of 14% solution

Answer 1

Darryl cannot make a 22 L 26% alcohol solution using the given 36% and 14% solutions.

Step-by-step explanation:

To find out how much of each solution Darryl must use, we can set up a system of equations. Let x represent the amount of the 36% alcohol solution, and y represent the amount of the 14% alcohol solution. We know that the total volume of the mixture is 22 L, so we have the equation x + y = 22. We also know that the concentration of the alcohol in the mixture is 26%, so we have the equation (0.36x + 0.14y) / 22 = 0.26. Solving this system of equations will give us the values of x and y.

Multiplying the first equation by 0.36, we get 0.36x + 0.36y = 7.92. Subtracting this equation from the second equation, we get (0.36x + 0.14y) - (0.36x + 0.36y) = 0.26 - 7.92. Simplifying, we get -0.22y = -7.66. Dividing both sides by -0.22, we find that y = 34.9091. Substituting this value of y into the first equation, we find that x = 22 - 34.9091 = -12.9091. However, since we cannot have a negative volume, this solution is not valid.

We can conclude that Darryl cannot make a 22 L 26% alcohol solution using the given 36% and 14% solutions.