I posted this problem earlier, but I still can't figure it out. It is for extra credit. I was hoping if someone could please solve it. I would greatly appreciate it.

A bourbon that is 51 proof is 25.5% alcohol by vol. while one that is 82 proof is 41% alcohol by vol. How many liters of 52 proof bourbon must be mixed with 1.0L of 82 proof bourbon to produce a 66 proof bourbon? Give answer to 3 decimal places.
Thanks in advance for all the help!

Let the volume of 52 proof to be added be x L

so .26x + .41(1) = .33(1+x)
or
26x + 41 = 33(1+x)
26x + 41 = 33 + 33x
8 = 7x
x = 8/7 = 1.143 L

check my arithmetic

To solve this problem, we can use the concept of mixture problems. In this case, we need to find the amount of 52 proof bourbon needed to mix with 1.0L of 82 proof bourbon to produce a 66 proof bourbon.

Let's break down the problem and write down the given information:
- Initial volume of 82 proof bourbon = 1.0L
- Proof of 82 proof bourbon = 82 (41% alcohol by volume)
- Proof of 52 proof bourbon (unknown) = ?

Now, let's set up the equation based on the concept that the total amount of alcohol in the mixture will remain the same:

(Alcohol in 82 proof bourbon) + (Alcohol in 52 proof bourbon) = (Alcohol in final mixture)

To solve for the amount of 52 proof bourbon needed, we need to find its volume. Let's represent the volume of 52 proof bourbon as "x" liters.

So now, let's set up the equation:

(1.0L * 82) + (x * 52) = (1.0L + x) * 66

Here's the explanation of the equation:

- The left side represents the total amount of alcohol in the mixture.
- The right side represents the total amount of alcohol in the final mixture.
- The proof of the 82 proof bourbon is multiplied by its volume (1.0L), and the proof of the 52 proof bourbon is multiplied by its volume (x).
- The sum of these two values on the left side should be equal to the total amount of alcohol in the final mixture, which is calculated by multiplying the proof of the final mixture (66) with its volume (1.0L + x).

Now, let's solve the equation for "x".

82 + 52x = 66(1 + x)
82 + 52x = 66 + 66x

Rearrange the equation to isolate "x".

52x - 66x = 66 - 82
-14x = -16

Divide both sides by -14 to solve for "x".

x = -16 / -14

Simplify to get the value of "x".

x = 8 / 7

x ≈ 1.143 (rounded to 3 decimal places)

Therefore, approximately 1.143 liters of 52 proof bourbon must be mixed with 1.0L of 82 proof bourbon to produce a 66 proof bourbon.