Let's break down the problem step by step:

Initial Conditions

• Gary has 400 ml of a drink that is 10% orange juice.
• Therefore, the amount of pure orange juice in the drink is: $\text{Orange juice} = 10\% \times 400 \text{ ml} = \frac{10}{100} \times 400 = 40 \text{ ml}$

Goal

• Gary wants to add some amount of orange juice $x$ to the drink so that the resulting drink is 12% orange juice.

New Conditions After Adding Orange Juice

• The total volume of the drink after adding $x$ ml of orange juice will be: $400 \text{ ml} + x \text{ ml}$
• The total amount of orange juice in the new mixture will be: $40 \text{ ml} + x \text{ ml}$
• We want the new mixture to be 12% orange juice: $\frac{40 + x}{400 + x} = 12\%$ $\frac{40 + x}{400 + x} = \frac{12}{100}$

Solving the Equation

Now, we solve for $x$: $\frac{40 + x}{400 + x} = \frac{12}{100}$ Cross-multiply to solve: $100(40 + x) = 12(400 + x)$ $4000 + 100x = 4800 + 12x$ Subtract $12x$ from both sides: $4000 + 88x = 4800$ Subtract 4000 from both sides: $88x = 800$ Solve for $x$: $x = \frac{800}{88} \approx 9.09 \text{ ml}$

Conclusion

Gary needs to add approximately 9.09 ml of extra orange juice to the jug to make the drink 12% orange juice.

Would you like to dive into the details, or do you have any questions?

Here are five related questions:

1. How would the required amount of orange juice change if Gary wanted 15% orange juice instead?
2. What if the initial drink had 8% orange juice instead of 10%?
3. How would the problem change if the total volume of the drink was 500 ml instead of 400 ml?
4. What if Gary had only 30 ml of orange juice available—could he still reach the 12% goal?
5. How would the solution change if Gary wanted the drink to be 12.5% orange juice?

Tip: When dealing with percentage problems, setting up the equation correctly is crucial for finding the correct solution.