Question

How many ounces of a 22% alcohol solution and a 45% alcohol solution must be combined to obtain 4y ounces of a 33% solution?

Answer 1

To obtain 4y ounces of a 33% solution, you would need approximately 15.82 ounces of the 22% alcohol solution and 4 ounces of the 45% alcohol solution.

Step-by-step explanation:

To solve this problem, we can set up an equation using the concept of the amount of alcohol in the solution. Let's say we need x ounces of the 22% alcohol solution and y ounces of the 45% alcohol solution. The equation would be:

0.22x + 0.45y = 0.33(4y)

Simplifying the equation, we get:

0.22x + 0.45y = 1.32y

0.22x = 0.87y

Now, we have two variables and one equation. To solve for x, we can substitute the value of y from the equation above into the first equation. Solving for x, we can find the number of ounces of the 22% alcohol solution needed.

For example, let's say we let y = 4. Plugging this value into the equation, we get:

0.22x + 0.45(4) = 1.32(4)

0.22x + 1.8 = 5.28

0.22x = 5.28 - 1.8

0.22x = 3.48

x = 3.48 / 0.22

x = 15.82

So, to obtain 4y ounces of a 33% solution, you would need approximately 15.82 ounces of the 22% alcohol solution and 4 ounces of the 45% alcohol solution.