Question

Organize each of the following equations to express P as a function of Q.

Q as a function of P P as a function of Q
Q=30-P P=30+Q, P=Q-30, P=30/Q, P=30-Q

Q=12-3P P=4-1/3Q, P=12-Q, P=-12+3Q, P=12+-3Q

8Q=18-2P P=9-4Q/8, P=9-4Q, P=18-2Q/8, P=18-2/8 Q

Answer 1

Let's rearrange each equation to express \( P \) as a function of \( Q \).

### 1. **For the equation \( Q = 30 - P \):**
To express \( P \) as a function of \( Q \), we need to isolate \( P \):

\[
Q = 30 - P
\]

Rearranging gives:

\[
P = 30 - Q
\]

So, we have:
\[
\text{P as a function of Q: } P = 30 - Q
\]

### 2. **For the equation \( Q = 12 - 3P \):**
Again, isolating \( P \):

\[
Q = 12 - 3P
\]

Rearranging gives:

\[
3P = 12 - Q
\]

Dividing by 3 gives:

\[
P = \frac{12 - Q}{3} = 4 - \frac{1}{3}Q
\]

So, we have:
\[
\text{P as a function of Q: } P = 4 - \frac{1}{3}Q
\]

### 3. **For the equation \( 8Q = 18 - 2P \):**
Isolate \( P \):

\[
8Q = 18 - 2P
\]

Rearranging gives:

\[
2P = 18 - 8Q
\]

Dividing by 2 gives:

\[
P = 9 - 4Q
\]

So, we have:
\[
\text{P as a function of Q: } P = 9 - 4Q
\]

### Summary

Here are the results:

- **Q as a function of P:**
- \( Q = 30 - P \)
- \( Q = 12 - 3P \)
- \( 8Q = 18 - 2P \) (which can be rearranged to \( Q = \frac{18 - 2P}{8} \))

- **P as a function of Q:**
- \( P = 30 - Q \)
- \( P = 4 - \frac{1}{3}Q \)
- \( P = 9 - 4Q \)