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The problem shows a proportional relationship between the cups of flour (\( x \)) and the number of cookies (\( y \)).

To find how many cookies can be made per cup of flour, we can use the fact that in a proportional relationship, \( y = kx \), where \( k \) is the constant of proportionality. This \( k \) represents the number of cookies per cup of flour.

We can determine \( k \) by using the values from the table:

For instance, when \( x = 3 \) cups of flour, \( y = 48 \) cookies. Using the formula:

\[
k = \frac{y}{x} = \frac{48}{3} = 16
\]

So, the constant \( k = 16 \), meaning 16 cookies can be made per cup of flour.

This result can be verified with other values in the table. For example:

- \( x = 6 \), \( y = 96 \):
  \[
  k = \frac{96}{6} = 16
  \]
- \( x = 7.5 \), \( y = 120 \):
  \[
  k = \frac{120}{7.5} = 16
  \]

In all cases, \( k = 16 \), confirming that 16 cookies are made per cup of flour.

Would you like more details or have any further questions?

### Related questions:
1. How do you calculate the constant of proportionality in any proportional relationship?
2. What would happen to the number of cookies if you used 10 cups of flour?
3. Can you express the proportional relationship as an equation?
4. How can we interpret the constant \( k \) in terms of the recipe?
5. If the number of cookies increased to 200, how many cups of flour would be needed?

**Tip:** In proportional relationships, once you find the constant of proportionality, you can predict any corresponding value of \( y \) from \( x \) by using the formula \( y = kx \).

Based on this relationship, how many cookies can be made per cup of flour?

Discover how to calculate the number of cookies made per cup of flour in a proportional relationship. The constant of proportionality is determined using key values from the table, showing that 16 cookies can be made per cup of flour. Suitable for middle school students, Grades 6-8.

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