If 2/3 of a liter of juice gives you 80% of your daily value of vitamin C, then how much juice
will give you 100% of your daily value of vitamin C? Show how to solve this problem with the aid of a math drawing and a percent table. Explain
your reasoning.

To solve this problem, we need to determine how much juice will give 100% of the daily value of vitamin C based on the fact that 2/3 of a liter provides 80%. We'll use a mathematical approach, including a percent table and a visual aid (which I'll describe), to help us understand the problem clearly.

### Step-by-step explanation:

1. **Define the known quantities:**
   - 2/3 of a liter of juice provides 80% of the daily value of vitamin C.
   - We need to find how much juice (in liters) will provide 100% of the daily value.

2. **Set up a proportion:**

   Let \( x \) be the amount of juice (in liters) that gives 100% of the daily value of vitamin C. Since 2/3 of a liter gives 80%, we can set up the following proportion:

   \[
   \frac{2/3}{80} = \frac{x}{100}
   \]

3. **Solve the proportion:**

   To solve for \( x \), we cross-multiply:

   \[
   (2/3) \times 100 = 80 \times x
   \]

   Simplify the equation:

   \[
   \frac{200}{3} = 80x
   \]

   Now, divide both sides by 80:

   \[
   x = \frac{200}{3 \times 80} = \frac{200}{240}
   \]

   Simplify the fraction:

   \[
   x = \frac{5}{6} \text{ liters}
   \]

   So, \( \frac{5}{6} \) liters of juice will provide 100% of the daily value of vitamin C.

---

### Percent Table:

| Percentage of Vitamin C | Juice (in liters) |
|-------------------------|-------------------|
| 80%                     | \( \frac{2}{3} \) liters |
| 100%                    | \( \frac{5}{6} \) liters |

- From the table, you can see the relationship between the percentage and the amount of juice. We started with 80% and \( \frac{2}{3} \) liters, and we found that 100% corresponds to \( \frac{5}{6} \) liters.

---

### Math Drawing (Description):

Imagine a rectangle divided into 5 equal parts. Each part represents 20% of the daily value of vitamin C:

- For 80%, you would shade 4 out of the 5 parts. This corresponds to \( \frac{2}{3} \) liters.
- To get 100%, you would need to shade the entire rectangle, which corresponds to \( \frac{5}{6} \) liters.

### Reasoning:

The proportion and the percent table both show how the juice's amount scales with the percentage of vitamin C. Since 80% corresponds to \( \frac{2}{3} \) liters, we set up a ratio to calculate the amount of juice that corresponds to 100%.

Would you like further clarification or more details?

### 5 Related Questions:
1. How would you calculate the amount of juice for 50% of the daily value of vitamin C?
2. How can you express the percentage increase from 80% to 100% in this context?
3. What if 1 liter of juice provided 120% of the daily value of vitamin C? How much juice would give 100%?
4. How would you explain the relationship between juice and vitamin C using a different mathematical method, like a graph?
5. If the juice's vitamin C content increased by 10%, how would the new proportions be calculated?

### Tip:
When working with percentages, setting up a proportion helps solve for unknown quantities by maintaining a consistent relationship between the variables.

If 2/3 of a liter of juice gives you 80% of your daily value of vitamin C, then how much juice will give you 100% of your daily value of vitamin C? Show how to solve this problem with the aid of a math drawing and a percent table. Explain your reasoning.

Discover how to solve a real-world problem involving proportions and percentages. Learn how to calculate how much juice provides 100% of your daily vitamin C, using a percent table and a visual math drawing. Suitable for students in Grades 5-7.

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