Question

P is partly constant and partly varies inversely as Q. If Q=9 when P=3 and Q=18 when P=9, find P when Q=12.

Answer 1

Identifying the constants in a partly constant and partly inverse relationship between P and Q, using given pairs of values and finding P for a new value of Q.

Step-by-step explanation:

The student's question is concerned with a partly constant and partly inversely variable relationship between two quantities, P and Q. Given two sets of values for P and Q, we can find the equation that models this relationship. Using the givens, P = 3 when Q = 9 and P = 9 when Q = 18:

1. Assume the equation has the form P = a + (b/Q), where a and b are constants to be determined.
2. Substitute the given values into the equation to create a system of equations.
3. Solve the system for a and b.

Plug in Q = 12 into the solved equation to find the corresponding value of P.