a certain drink contains only 10% of mango juice. how much juice in litres has to be added to one litres of this drink so that the new mixture will contain 40% of mango juice

Let:
- \( x \) be the amount of mango juice (in liters) to be added to the 1 liter of drink.

Currently, the drink contains:
- 10% mango juice, so \( 0.1 \) liters of mango juice.

After adding \( x \) liters of pure mango juice, the total volume of the mixture will be:
- \( 1 + x \) liters.

We want the mango juice to make up 40% of the total volume. This leads to the equation:

\[
\frac{0.1 + x}{1 + x} = 0.4
\]

To solve for \( x \):
1. Multiply both sides by \( 1 + x \):

   \[
   0.1 + x = 0.4(1 + x)
   \]

2. Expand and simplify:

   \[
   0.1 + x = 0.4 + 0.4x
   \]

3. Move all terms involving \( x \) to one side:

   \[
   x - 0.4x = 0.4 - 0.1
   \]

   \[
   0.6x = 0.3
   \]

4. Divide by \( 0.6 \):

   \[
   x = \frac{0.3}{0.6} = 0.5
   \]

Thus, **0.5 liters of pure mango juice** needs to be added to achieve 40% mango juice in the mixture.

Would you like further clarification, or do you have more questions?

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Here are 5 related questions:
1. How would the calculation change if we wanted 50% mango juice in the mixture?
2. What if the initial drink had only 5% mango juice?
3. How can we find the percentage if we added 1 liter of mango juice instead?
4. What if we started with 2 liters of the initial 10% juice drink?
5. How does this relate to problems involving ratios and percentages in mixtures?

**Tip:** For mixture problems, setting up equations based on percentages helps ensure accurate results.

A certain drink contains only 10% of mango juice. How much juice in litres has to be added to one litre of this drink so that the new mixture will contain 40% of mango juice?

Learn how to calculate the amount of pure mango juice needed to increase the concentration from 10% to 40% in a 1-liter drink. This problem involves key algebraic concepts, including ratios and percentages, and is suitable for students in Grades 8-10.

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