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The problem in the image involves proportions and figuring out how many boxes of brownies Tyana can make given a certain ratio of flour. Let's break down the solution step by step:

### Problem:
Tyana has 6 cups of flour. The recipe uses a certain ratio to calculate the number of brownies she can make with 6 cups of flour. You are asked to identify which proportion will calculate how many boxes of brownies Tyana can make.

The key piece of information provided is that \( \frac{4}{3} \) is the ratio of flour to boxes of brownies. This ratio means that for every 4 cups of flour, Tyana can make 3 boxes of brownies.

### Proportions:
The question asks which proportion can be used to calculate how many boxes can be made with 6 cups of flour. There are four options:
- (a) \( \frac{4}{3} = \frac{6}{x} \)
- (b) \( \frac{4}{x} = \frac{3}{6} \)
- (c) \( \frac{4}{6} = \frac{x}{3} \)
- (d) \( \frac{3}{4} = \frac{x}{6} \)

### Solution:
To solve the problem, you should set up a proportion that relates flour and the number of boxes of brownies:
- We know the ratio is \( \frac{4 \, \text{cups of flour}}{3 \, \text{boxes of brownies}} \).
- Tyana has 6 cups of flour, so we need to figure out how many boxes, \( x \), this corresponds to.

We can set up the correct proportion like this:
\[
\frac{4}{3} = \frac{6}{x}
\]
This proportion (option a) is the correct one because it directly compares the known ratio to the unknown number of boxes.

### Solving for \( x \):
Now, let's solve for \( x \):
\[
\frac{4}{3} = \frac{6}{x}
\]
Cross-multiply:
\[
4x = 3 \times 6
\]
\[
4x = 18
\]
\[
x = \frac{18}{4} = 4.5
\]
So, Tyana can make 4.5 boxes of brownies with 6 cups of flour.

### Correct answer:
The correct answer is (a) \( \frac{4}{3} = \frac{6}{x} \).

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Let me know if you would like further details or have any questions.

Here are 5 related questions to deepen your understanding:
1. How would the proportion change if Tyana had 8 cups of flour instead of 6?
2. If the recipe called for 5 cups of flour for 3 boxes, how would that affect the ratio?
3. Can you solve \( \frac{5}{4} = \frac{x}{8} \) to find the value of \( x \)?
4. What would happen to the ratio if the recipe could make 5 boxes of brownies with 4 cups of flour?
5. How can you verify the answer by substituting \( x = 4.5 \) back into the original equation?

**Tip:** Always make sure your proportions match up in terms of units (flour to brownies in this case) before solving.

Tyana has 6 cups of flour and uses a certain ratio of flour to brownies to calculate how many boxes she can make. Which proportion from the given options can be used to find the number of boxes?

Learn how to solve a proportion problem where Tyana calculates the number of brownie boxes she can make using 6 cups of flour. The ratio of flour to brownies is 4 to 3. Solve using cross multiplication and proportions. Suitable for students in Grades 6-8.

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