Let's solve the problem step by step.

Step 1: Define the variables

Let $x$ be the percentage of fruit juice in Brand A.

Step 2: Set up the equation

• Kali mixed 9 gallons of Brand A with 6 gallons of Brand B.
• Brand B contains 5% fruit juice.
• The final mixture has 11% fruit juice.

The total amount of juice in the mixture comes from both Brand A and Brand B.

The equation for the total amount of fruit juice in the mixture is: $\text{Total juice in the mixture} = \text{Juice from Brand A} + \text{Juice from Brand B}$

This can be written as: $\text{Total juice} = \left(\frac{x}{100} \times 9\right) + \left(\frac{5}{100} \times 6\right)$

Step 3: Express the total juice in the mixture

The mixture contains 15 gallons (9 + 6) and 11% of this is fruit juice: $\frac{11}{100} \times 15$

Step 4: Set up the equation

Now, set up the equation with the expressions for the juice from Brand A and Brand B: $\frac{11}{100} \times 15 = \frac{x}{100} \times 9 + \frac{5}{100} \times 6$

Step 5: Solve for $x$

First, calculate the left-hand side: $\frac{11}{100} \times 15 = 1.65$

Next, calculate the contribution of Brand B: $\frac{5}{100} \times 6 = 0.3$

Now, substitute these values into the equation: $1.65 = \frac{9x}{100} + 0.3$

Subtract 0.3 from both sides: $1.35 = \frac{9x}{100}$

Multiply both sides by 100 to solve for $9x$: $135 = 9x$

Finally, divide both sides by 9: $x = 15$

Conclusion

The percentage of fruit juice in Brand A is 15%.

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Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How would the percentage change if more Brand A was added to the mixture?
2. What if Brand B had a different percentage of fruit juice? How would that affect the calculation?
3. How can we determine the total volume of fruit juice in the final mixture?
4. What is the importance of understanding concentration in mixtures?
5. How would the problem change if Brand A also had a known percentage of fruit juice?

Tip: When dealing with mixtures, always check the total volume and concentration to set up the correct equation.