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Let's solve the three parts of the problem step by step.

### a) Calculate \( M \) with \( w = 2 \) and \( p = 3.5 \)

The formula given is:

\[
M = wp + 6
\]

Substituting \( w = 2 \) and \( p = 3.5 \):

\[
M = 2 \times 3.5 + 6
\]

Calculate:

\[
M = 7 + 6 = 13
\]

So, \( M = 13 \).

### b) Rearrange the formula to solve for \( p \)

We start with the given formula:

\[
M = wp + 6
\]

To solve for \( p \), we first subtract 6 from both sides:

\[
M - 6 = wp
\]

Now, divide both sides by \( w \):

\[
p = \frac{M - 6}{w}
\]

So the formula for \( p \) is:

\[
p = \frac{M - 6}{w}
\]

### c) Calculate \( p \) for \( M = 15 \) and \( w = 3 \)

Using the formula we derived in part b:

\[
p = \frac{M - 6}{w}
\]

Substituting \( M = 15 \) and \( w = 3 \):

\[
p = \frac{15 - 6}{3}
\]

Calculate:

\[
p = \frac{9}{3} = 3
\]

So, \( p = 3 \).

Would you like more detailed explanations for any part of these calculations? Here are some related questions for further exploration:

1. What if \( w \) or \( p \) were negative? How would that affect the value of \( M \)?
2. How can we graph the function \( M = wp + 6 \) for different values of \( w \) and \( p \)?
3. What is the significance of the constant \( 6 \) in the formula?
4. How would you solve \( M \) if given an inequality involving \( w \) and \( p \)?
5. Could we interpret \( M, w, \) and \( p \) in a practical, real-world context?

**Tip**: When dealing with algebraic formulas, it's helpful to isolate the desired variable step-by-step by performing inverse operations in the correct order.

Sử dụng công thức M = wp + 6 để tính M với w = 2 và p = 3.5. Biến đổi công thức để lập công thức với p là chủ thể. Tính giá trị của p với M = 15 và w = 3.

Learn how to solve the linear equation M = wp + 6 with given values of w and p. This problem covers fundamental algebraic concepts and includes a step-by-step solution for both calculating M and rearranging the formula to solve for p.

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