To solve this problem, we will use a mixture equation based on the concentration of lemon juice.

Step 1: Define Variables

Let:

• $x$: liters of homemade lemonade (31% lemon juice)
• $y$: liters of store-bought lemonade (26% lemon juice)

From the total amount of lemonade:
$x + y = 24$

Step 2: Set Up the Mixture Equation

The total amount of lemon juice from each type must equal the lemon juice in the final mixture:
$0.31x + 0.26y = 0.27 \times 24$

Simplify the right-hand side:
$0.31x + 0.26y = 6.48$

Step 3: Solve the System of Equations

1. From the first equation:
   $y = 24 - x$
2. Substitute into the second equation:
   $0.31x + 0.26(24 - x) = 6.48$
3. Expand:
   $0.31x + 6.24 - 0.26x = 6.48$
4. Combine like terms:
   $0.05x = 0.24$
5. Solve for $x$:
   $x = \frac{0.24}{0.05} = 4.8$

Step 4: Find $y$

$y = 24 - 4.8 = 19.2$

Final Answer:

• Homemade lemonade: 4.8 liters
• Store-bought lemonade: 19.2 liters

Would you like more explanation or have questions?

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Related Questions:

1. How do you calculate percentages in mixture problems?
2. What are the key steps in solving a system of linear equations?
3. How does concentration affect mixture problems?
4. What happens if the desired concentration is higher than both sources?
5. How do you handle mixtures with more than two components?

Tip: When solving mixture problems, always set up equations for both the total quantity and the concentration to form a solvable system.