To solve the problem, we start with the relationship given by the variation statement. Since x varies jointly as y and z, we can express this as:
x = k * y * z
where k is the constant of variation.
We know that x = 8 when y = 4 and z = 9. We can use these values to find k:
8 = k * 4 * 9
Calculating the right side:
8 = k * 36
To find k, we divide both sides by 36:
k = 8 / 36 = 2 / 9
Now that we have the value of k, we can use this to find z when x = 16 and y = 6. We plug in the known values into the variation equation:
16 = (2 / 9) * 6 * z
First, calculate (2 / 9) * 6:
(2 / 9) * 6 = 12 / 9 = 4 / 3
Now we substitute this back into the equation:
16 = (4 / 3) * z
To solve for z, multiply both sides by (3 / 4):
z = 16 * (3 / 4) = 12
Therefore, when x = 16 and y = 6, z is equal to 12.