The problem tells us that p varies jointly as q and r. This type of variation is modeled by the equation p = kqr, where k is the constant of variation.
First, we can find the constant of variation using the given values where p=150, q=18, and r=5. We substitute these values into the equation:
150 = k * 18 * 5
We solve for k by dividing both sides of the equation by (18 * 5) = 90. This gives us k = 150 / 90 = 1.6666666666666667.
Now we are asked to find the value of q when p = 345 and r = 9.
We substitute these values and the value of k we just found into the equation. This gives us:
345 = 1.6666666666666667 * q * 9
We solve for q by dividing both sides of the equation by (1.6666666666666667 * 9) = 15. This gives us q = 345 / 15 = 23.
Therefore, when p = 345 and r = 9, the value of q is 23.