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

Question

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:

  • \( P = 30 - Q \)
  • \( P = 4 - \frac{1}{3}Q \)
  • \( P = 9 - 4Q \)